Random Intercept micro-macro APIM using lavaan (R)

background reading.

For introduction to RI-CLPM see: (Hamaker, Kuiper, and Grasman 2015)
Download Hamaker2015.pdf

For extensions of the RI-CLPM see: (Mulder and Hamaker 2020)
Download Mulder2020.pdf

Setup

Below you can find the code for installing and loading the required package lavaan (Rosseel 2012), as well as for reading in the data for the Random Intercept Cross-Lagged Panel Model (RI-CLPM) and its 3 extensions. You can specify the path to the data yourself, or through a menu by using the file.choose()-function. You can download the simulated example datasets here.

Download the liss dataset here:

Download lisscd_riclpm_testdata.Rdata

# If necessary, install the 'Lavaan' package. 
# install.packages('lavaan', dependencies = T)
# Load the required packages. 

rm(list=ls())

require(lavaan) 

# Load in the data. 
## Traditional RI-CLPM
dat <- read.table("data/RICLPM.dat", 
                  col.names = c("x1", "x2", "x3", "x4", "x5", "y1", "y2", "y3", "y4", "y5")) 
## Extension 1
datZ <- read.table("data/RICLPM-Z.dat",
                   col.names = c("x1", "x2", "x3", "x4", "x5", "y1", "y2", "y3", "y4", "y5", "z2", "z1"))
## Extension 2
datMG <- read.table("data/RICLPM-MG.dat",
                    col.names = c("x1", "x2", "x3", "x4", "x5", "y1", "y2", "y3", "y4", "y5", "G")) 
## Extension 3
datMI <- read.table("data/RICLPM-MI.dat",
                   col.names = c("x11", "x12", "x13",
                                 "x21", "x22", "x23",
                                 "x31", "x32", "x33",
                                 "x41", "x42", "x43",
                                 "x51", "x52", "x53", 
                                
                                 "y11", "y12", "y13",
                                 "y21", "y22", "y23",
                                 "y31", "y32", "y33", 
                                 "y41", "y42", "y43", 
                                 "y51", "y52", "y53"))

load('data/lisscd_riclpm_testdata.Rdata')
# Een _ gevolgd door een cijfer geeft de survey wave aan. Een . gevolgd door een cijfer geeft de alter aan. Dus educalter_1.4 in de wide file betekent de opleiding van alter 4 in surveywave 1. Waarom deze volgorde en niet andersom? Nu kan je makkelijk van wide naar long omzetten en viceversa.  

#data liss wide
datalw <- lisscdn_mlsem_wide

#select only respondents with no missing on dependent variable in the last 5 waves. 
datalw <- datalw[complete.cases(cbind(datalw$eu_7,datalw$eu_8,datalw$eu_9,datalw$eu_10,datalw$eu_11)),]

Goals

• compare standard two-wave APIM with CLPM.
  • outcome: same model
• compare five-wave APIM/CLPM with two-wave APIM/CLPM
  • outcome: cross-lagged effect of educalter ~ eu is now stronger than eu ~ educalter!
• compare five-wave CLPM with five-wave RI-CLPM
  • outcome: cross-lagged effect of eu ~ educalter is no longer significant in RI-CLPM!
• compare five-wave CLPM with one indicator with five-wave CLPM with multiple indicators (one model and two-step)
  • when we use multiple indicators in one step we find the results we expect to see.
    
  • In two-step approach cross-lagged paths are similar in strength.
    
  • I am unsure about the preferred approach. My guess is that the two-step approach is closer to the bias corrected means idea of the micro-macro model.
• compare five-wave CLPM with multiple indicator with RI-CLPM with multiple indicators.
  • comparison of two-step approach:
    
  • comparison of one-step approach

calculate the (bias corrected) means for use later.

To estimate the bias corrected means over time. Do we need/want to add the covariances between the latent factors?? We also assume local independence; the educational level of the confidants are independent given the ‘mean’ educational level of the CDN. Following a SNA perspective this is actually quite unlikely.

mulder hamaker data

myModel <- '  
  #####################
  # MEASUREMENT MODEL #
  #####################
  
  # Factor models for x at 5 waves (constrained). 
  FX1 =~ a*x11 + b*x12 + c*x13
  FX2 =~ a*x21 + b*x22 + c*x23
  FX3 =~ a*x31 + b*x32 + c*x33
  FX4 =~ a*x41 + b*x42 + c*x43
  FX5 =~ a*x51 + b*x52 + c*x53
  
  # Factor models for y at 5 waves (constrained).
  FY1 =~ d*y11 + e*y12 + f*y13
  FY2 =~ d*y21 + e*y22 + f*y23
  FY3 =~ d*y31 + e*y32 + f*y33
  FY4 =~ d*y41 + e*y42 + f*y43
  FY5 =~ d*y51 + e*y52 + f*y53
  
  # Constrained intercepts over time (this is necessary for strong factorial 
  # invariance; without these contraints we have week factorial invariance). 
  x11 + x21 + x31 + x41 + x51 ~ g*1
  x12 + x22 + x32 + x42 + x52 ~ h*1
  x13 + x23 + x33 + x43 + x53 ~ i*1
  y11 + y21 + y31 + y41 + y51 ~ j*1
  y12 + y22 + y32 + y42 + y52 ~ k*1
  y13 + y23 + y33 + y43 + y53 ~ l*1
  
  # Free latent means from t = 2 onward (only do this in combination with the 
  # constraints on the intercepts; without these, this would not be specified).
  # I DONT UNDERSTAND THIS. IF YOU HAVE CONSTRAINED INTERCEPTS AND CONSTRAINED FACTOR LOADINGS YOU WILL GET SIMILAR MEANS??!!
  # NO THIS IS NOT HOW IT WORKS IN SEM. IF YOU INCLUDE INTERCEPTS ONLY DEVIATIONS FROM THIS INTERCEPT PREDICT THE FACTOR LOADINGS. 
  # YOU ALSO SEE THIS IN THE RESULTS. INCLUDING INTERCEPTS LEADS TO SIMILAR MEANS ACROSS FX. CONSTRAINING ALLOWS FOR CHANGING MEANS. 
  FX2 + FX3 + FX4 + FX5 + FY2 + FY3 + FY4 + FY5 ~ 1
  
  
'



RICLPM5.ext3.fit <- cfa(myModel, data = datMI, missing = 'ML')

  # WHY WOULD WE WANT TO INCLUDE ALL VARIANCES AND COVARIANCES BETWEEN FACTORS?? 
summary(RICLPM5.ext3.fit, standardized = T)

#> lavaan 0.6-7 ended normally after 122 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of free parameters                        143
#>   Number of equality constraints                    40
#>                                                       
#>   Number of observations                          1189
#>   Number of missing patterns                         1
#>                                                       
#> Model Test User Model:
#>                                                       
#>   Test statistic                               368.981
#>   Degrees of freedom                               392
#>   P-value (Chi-square)                           0.792
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Observed
#>   Observed information based on                Hessian
#> 
#> Latent Variables:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   FX1 =~                                                                
#>     x11        (a)    1.000                               0.293    0.390
#>     x12        (b)    0.842    0.098    8.577    0.000    0.247    0.316
#>     x13        (c)    0.778    0.091    8.571    0.000    0.228    0.308
#>   FX2 =~                                                                
#>     x21        (a)    1.000                               0.219    0.301
#>     x22        (b)    0.842    0.098    8.577    0.000    0.184    0.248
#>     x23        (c)    0.778    0.091    8.571    0.000    0.170    0.238
#>   FX3 =~                                                                
#>     x31        (a)    1.000                               0.247    0.349
#>     x32        (b)    0.842    0.098    8.577    0.000    0.208    0.291
#>     x33        (c)    0.778    0.091    8.571    0.000    0.192    0.253
#>   FX4 =~                                                                
#>     x41        (a)    1.000                               0.267    0.354
#>     x42        (b)    0.842    0.098    8.577    0.000    0.225    0.302
#>     x43        (c)    0.778    0.091    8.571    0.000    0.208    0.276
#>   FX5 =~                                                                
#>     x51        (a)    1.000                               0.236    0.319
#>     x52        (b)    0.842    0.098    8.577    0.000    0.199    0.265
#>     x53        (c)    0.778    0.091    8.571    0.000    0.184    0.250
#>   FY1 =~                                                                
#>     y11        (d)    1.000                               0.291    0.373
#>     y12        (e)    1.125    0.082   13.746    0.000    0.327    0.417
#>     y13        (f)    1.130    0.080   14.163    0.000    0.329    0.425
#>   FY2 =~                                                                
#>     y21        (d)    1.000                               0.316    0.410
#>     y22        (e)    1.125    0.082   13.746    0.000    0.356    0.477
#>     y23        (f)    1.130    0.080   14.163    0.000    0.357    0.442
#>   FY3 =~                                                                
#>     y31        (d)    1.000                               0.267    0.353
#>     y32        (e)    1.125    0.082   13.746    0.000    0.301    0.382
#>     y33        (f)    1.130    0.080   14.163    0.000    0.302    0.380
#>   FY4 =~                                                                
#>     y41        (d)    1.000                               0.295    0.376
#>     y42        (e)    1.125    0.082   13.746    0.000    0.332    0.429
#>     y43        (f)    1.130    0.080   14.163    0.000    0.334    0.434
#>   FY5 =~                                                                
#>     y51        (d)    1.000                               0.310    0.398
#>     y52        (e)    1.125    0.082   13.746    0.000    0.349    0.440
#>     y53        (f)    1.130    0.080   14.163    0.000    0.350    0.453
#> 
#> Covariances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   FX1 ~~                                                                
#>     FX2               0.034    0.009    3.684    0.000    0.532    0.532
#>     FX3               0.019    0.008    2.321    0.020    0.269    0.269
#>     FX4               0.019    0.009    2.182    0.029    0.249    0.249
#>     FX5               0.008    0.008    1.007    0.314    0.122    0.122
#>     FY1               0.007    0.008    0.959    0.338    0.086    0.086
#>     FY2               0.019    0.008    2.361    0.018    0.201    0.201
#>     FY3               0.013    0.008    1.769    0.077    0.171    0.171
#>     FY4               0.024    0.008    3.017    0.003    0.275    0.275
#>     FY5               0.006    0.008    0.811    0.417    0.070    0.070
#>   FX2 ~~                                                                
#>     FX3               0.026    0.008    3.159    0.002    0.483    0.483
#>     FX4               0.020    0.008    2.482    0.013    0.350    0.350
#>     FX5               0.012    0.008    1.502    0.133    0.234    0.234
#>     FY1              -0.000    0.007   -0.014    0.989   -0.002   -0.002
#>     FY2               0.006    0.007    0.898    0.369    0.093    0.093
#>     FY3               0.021    0.007    2.955    0.003    0.360    0.360
#>     FY4               0.024    0.007    3.323    0.001    0.375    0.375
#>     FY5               0.019    0.007    2.577    0.010    0.279    0.279
#>   FX3 ~~                                                                
#>     FX4               0.037    0.009    3.914    0.000    0.558    0.558
#>     FX5               0.021    0.009    2.430    0.015    0.358    0.358
#>     FY1               0.016    0.007    2.226    0.026    0.223    0.223
#>     FY2               0.001    0.007    0.160    0.873    0.015    0.015
#>     FY3               0.015    0.007    2.102    0.036    0.226    0.226
#>     FY4               0.009    0.007    1.327    0.185    0.130    0.130
#>     FY5               0.019    0.007    2.558    0.011    0.248    0.248
#>   FX4 ~~                                                                
#>     FX5               0.025    0.009    2.828    0.005    0.399    0.399
#>     FY1               0.020    0.008    2.649    0.008    0.258    0.258
#>     FY2               0.009    0.008    1.248    0.212    0.112    0.112
#>     FY3               0.017    0.007    2.254    0.024    0.233    0.233
#>     FY4               0.014    0.008    1.872    0.061    0.178    0.178
#>     FY5               0.019    0.008    2.404    0.016    0.225    0.225
#>   FX5 ~~                                                                
#>     FY1               0.013    0.007    1.807    0.071    0.192    0.192
#>     FY2               0.003    0.007    0.427    0.669    0.042    0.042
#>     FY3               0.021    0.007    2.849    0.004    0.328    0.328
#>     FY4               0.014    0.007    1.893    0.058    0.200    0.200
#>     FY5               0.019    0.007    2.501    0.012    0.255    0.255
#>   FY1 ~~                                                                
#>     FY2               0.036    0.008    4.795    0.000    0.394    0.394
#>     FY3               0.024    0.007    3.456    0.001    0.309    0.309
#>     FY4               0.026    0.007    3.733    0.000    0.306    0.306
#>     FY5               0.020    0.007    2.890    0.004    0.224    0.224
#>   FY2 ~~                                                                
#>     FY3               0.052    0.008    6.152    0.000    0.611    0.611
#>     FY4               0.046    0.008    5.832    0.000    0.488    0.488
#>     FY5               0.029    0.008    3.875    0.000    0.299    0.299
#>   FY3 ~~                                                                
#>     FY4               0.052    0.008    6.408    0.000    0.657    0.657
#>     FY5               0.039    0.008    5.078    0.000    0.469    0.469
#>   FY4 ~~                                                                
#>     FY5               0.050    0.008    5.924    0.000    0.543    0.543
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>    .x11        (g)    0.272    0.018   15.091    0.000    0.272    0.362
#>    .x21        (g)    0.272    0.018   15.091    0.000    0.272    0.375
#>    .x31        (g)    0.272    0.018   15.091    0.000    0.272    0.384
#>    .x41        (g)    0.272    0.018   15.091    0.000    0.272    0.360
#>    .x51        (g)    0.272    0.018   15.091    0.000    0.272    0.368
#>    .x12        (h)    0.253    0.017   15.141    0.000    0.253    0.324
#>    .x22        (h)    0.253    0.017   15.141    0.000    0.253    0.340
#>    .x32        (h)    0.253    0.017   15.141    0.000    0.253    0.353
#>    .x42        (h)    0.253    0.017   15.141    0.000    0.253    0.339
#>    .x52        (h)    0.253    0.017   15.141    0.000    0.253    0.337
#>    .x13        (i)    0.268    0.016   16.836    0.000    0.268    0.363
#>    .x23        (i)    0.268    0.016   16.836    0.000    0.268    0.376
#>    .x33        (i)    0.268    0.016   16.836    0.000    0.268    0.353
#>    .x43        (i)    0.268    0.016   16.836    0.000    0.268    0.356
#>    .x53        (i)    0.268    0.016   16.836    0.000    0.268    0.365
#>    .y11        (j)    0.324    0.016   20.302    0.000    0.324    0.416
#>    .y21        (j)    0.324    0.016   20.302    0.000    0.324    0.421
#>    .y31        (j)    0.324    0.016   20.302    0.000    0.324    0.428
#>    .y41        (j)    0.324    0.016   20.302    0.000    0.324    0.413
#>    .y51        (j)    0.324    0.016   20.302    0.000    0.324    0.417
#>    .y12        (k)    0.331    0.017   19.180    0.000    0.331    0.422
#>    .y22        (k)    0.331    0.017   19.180    0.000    0.331    0.445
#>    .y32        (k)    0.331    0.017   19.180    0.000    0.331    0.421
#>    .y42        (k)    0.331    0.017   19.180    0.000    0.331    0.427
#>    .y52        (k)    0.331    0.017   19.180    0.000    0.331    0.418
#>    .y13        (l)    0.325    0.017   18.799    0.000    0.325    0.421
#>    .y23        (l)    0.325    0.017   18.799    0.000    0.325    0.402
#>    .y33        (l)    0.325    0.017   18.799    0.000    0.325    0.409
#>    .y43        (l)    0.325    0.017   18.799    0.000    0.325    0.422
#>    .y53        (l)    0.325    0.017   18.799    0.000    0.325    0.420
#>     FX2              -0.077    0.021   -3.731    0.000   -0.354   -0.354
#>     FX3              -0.074    0.022   -3.425    0.001   -0.298   -0.298
#>     FX4              -0.158    0.023   -6.781    0.000   -0.591   -0.591
#>     FX5              -0.180    0.024   -7.577    0.000   -0.762   -0.762
#>     FY2               0.034    0.018    1.898    0.058    0.109    0.109
#>     FY3               0.016    0.018    0.897    0.370    0.062    0.062
#>     FY4               0.048    0.019    2.595    0.009    0.163    0.163
#>     FY5               0.053    0.019    2.771    0.006    0.170    0.170
#>     FX1               0.000                               0.000    0.000
#>     FY1               0.000                               0.000    0.000
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>    .x11               0.478    0.026   18.514    0.000    0.478    0.848
#>    .x12               0.549    0.026   21.013    0.000    0.549    0.900
#>    .x13               0.494    0.023   21.379    0.000    0.494    0.905
#>    .x21               0.480    0.024   20.148    0.000    0.480    0.909
#>    .x22               0.519    0.024   22.042    0.000    0.519    0.939
#>    .x23               0.480    0.022   22.252    0.000    0.480    0.943
#>    .x31               0.440    0.023   19.102    0.000    0.440    0.878
#>    .x32               0.469    0.022   21.244    0.000    0.469    0.915
#>    .x33               0.539    0.024   22.545    0.000    0.539    0.936
#>    .x41               0.499    0.025   19.750    0.000    0.499    0.875
#>    .x42               0.506    0.024   21.230    0.000    0.506    0.909
#>    .x43               0.524    0.024   21.600    0.000    0.524    0.924
#>    .x51               0.491    0.025   19.541    0.000    0.491    0.898
#>    .x52               0.523    0.024   21.840    0.000    0.523    0.930
#>    .x53               0.505    0.023   21.978    0.000    0.505    0.937
#>    .y11               0.522    0.025   21.148    0.000    0.522    0.861
#>    .y12               0.509    0.025   19.959    0.000    0.509    0.826
#>    .y13               0.488    0.025   19.419    0.000    0.488    0.819
#>    .y21               0.494    0.024   20.897    0.000    0.494    0.832
#>    .y22               0.428    0.023   18.918    0.000    0.428    0.772
#>    .y23               0.525    0.026   20.092    0.000    0.525    0.804
#>    .y31               0.502    0.023   21.595    0.000    0.502    0.875
#>    .y32               0.528    0.026   20.638    0.000    0.528    0.854
#>    .y33               0.541    0.026   21.060    0.000    0.541    0.856
#>    .y41               0.529    0.025   21.372    0.000    0.529    0.858
#>    .y42               0.490    0.024   20.125    0.000    0.490    0.816
#>    .y43               0.480    0.024   20.203    0.000    0.480    0.812
#>    .y51               0.509    0.024   20.851    0.000    0.509    0.841
#>    .y52               0.506    0.026   19.822    0.000    0.506    0.806
#>    .y53               0.475    0.025   19.220    0.000    0.475    0.795
#>     FX1               0.086    0.017    4.897    0.000    1.000    1.000
#>     FX2               0.048    0.014    3.477    0.001    1.000    1.000
#>     FX3               0.061    0.015    4.120    0.000    1.000    1.000
#>     FX4               0.071    0.016    4.582    0.000    1.000    1.000
#>     FX5               0.056    0.015    3.730    0.000    1.000    1.000
#>     FY1               0.085    0.013    6.728    0.000    1.000    1.000
#>     FY2               0.100    0.014    7.314    0.000    1.000    1.000
#>     FY3               0.071    0.012    6.060    0.000    1.000    1.000
#>     FY4               0.087    0.013    6.732    0.000    1.000    1.000
#>     FY5               0.096    0.014    7.063    0.000    1.000    1.000

# 2. extract the predicted values of the cfa and add them to new dataframe data_wide2
datMIb <- data.frame(datMI, predict(RICLPM5.ext3.fit))

liss data

aggregated means

datalw$Meducalter_7 <- rowMeans(cbind(datalw$educalter_7.1, datalw$educalter_7.2, datalw$educalter_7.3, 
    datalw$educalter_7.4, datalw$educalter_7.5), na.rm = T)

summary(datalw$Meducalter_7)

#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
#>    4.00   10.50   12.00   12.14   13.75   16.00     390

datalw$Meducalter_8 <- rowMeans(cbind(datalw$educalter_8.1, datalw$educalter_8.2, datalw$educalter_8.3, 
    datalw$educalter_8.4, datalw$educalter_8.5), na.rm = T)

datalw$Meducalter_9 <- rowMeans(cbind(datalw$educalter_9.1, datalw$educalter_9.2, datalw$educalter_9.3, 
    datalw$educalter_9.4, datalw$educalter_9.5), na.rm = T)

datalw$Meducalter_10 <- rowMeans(cbind(datalw$educalter_10.1, datalw$educalter_10.2, datalw$educalter_10.3, 
    datalw$educalter_10.4, datalw$educalter_10.5), na.rm = T)

datalw$Meducalter_11 <- rowMeans(cbind(datalw$educalter_11.1, datalw$educalter_11.2, datalw$educalter_11.3, 
    datalw$educalter_11.4, datalw$educalter_11.5), na.rm = T)

bias corrected means

• alters are identical thus equal loadings, variances and intercepts at each time point.
  
• Free latent means from t = 2 onward, to allow time trends.
  
• be aware that respondents with no confidants in a specific wave will get a score in the below approach. this means way less missings!! HOW DID THIJMEN DEAL WITH THIS??

myModel <- '

  #alters are identical thus equal loadings, variances and intercepts at each time point. 
  
  #constrained loadings
  Feducalter_7 =~ 1*educalter_7.1 + 1*educalter_7.2 + 1*educalter_7.3 +  1*educalter_7.4 + 1*educalter_7.5
  Feducalter_8 =~ 1*educalter_8.1 + 1*educalter_8.2 + 1*educalter_8.3 +  1*educalter_8.4 + 1*educalter_8.5
  Feducalter_9 =~ 1*educalter_9.1 + 1*educalter_9.2 + 1*educalter_9.3 +  1*educalter_9.4 + 1*educalter_9.5
  Feducalter_10 =~ 1*educalter_10.1 + 1*educalter_10.2 + 1*educalter_10.3 +  1*educalter_10.4 + 1*educalter_10.5
  Feducalter_11 =~ 1*educalter_11.1 + 1*educalter_11.2 + 1*educalter_11.3 +  1*educalter_11.4 + 1*educalter_11.5
  
  Feducalter_7 ~~ Feducalter_7
  Feducalter_8 ~~ Feducalter_8
  Feducalter_9 ~~ Feducalter_9
  Feducalter_10 ~~ Feducalter_10
  Feducalter_11 ~~ Feducalter_11
  
  #constrained variances
  educalter_7.1 ~~ e*educalter_7.1
  educalter_7.2 ~~ e*educalter_7.2
  educalter_7.3 ~~ e*educalter_7.3
  educalter_7.4 ~~ e*educalter_7.4
  educalter_7.5 ~~ e*educalter_7.5
  
  educalter_8.1 ~~ f*educalter_8.1
  educalter_8.2 ~~ f*educalter_8.2
  educalter_8.3 ~~ f*educalter_8.3
  educalter_8.4 ~~ f*educalter_8.4
  educalter_8.5 ~~ f*educalter_8.5
  
  educalter_9.1 ~~ g*educalter_9.1
  educalter_9.2 ~~ g*educalter_9.2
  educalter_9.3 ~~ g*educalter_9.3
  educalter_9.4 ~~ g*educalter_9.4
  educalter_9.5 ~~ g*educalter_9.5
  
  educalter_10.1 ~~ h*educalter_10.1
  educalter_10.2 ~~ h*educalter_10.2
  educalter_10.3 ~~ h*educalter_10.3
  educalter_10.4 ~~ h*educalter_10.4
  educalter_10.5 ~~ h*educalter_10.5
  
  educalter_11.1 ~~ i*educalter_11.1
  educalter_11.2 ~~ i*educalter_11.2
  educalter_11.3 ~~ i*educalter_11.3
  educalter_11.4 ~~ i*educalter_11.4
  educalter_11.5 ~~ i*educalter_11.5
  
  #constrained intercepts / we want structural changes to be picked up by the factor
  educalter_7.1 ~ j*1
  educalter_7.2 ~ j*1
  educalter_7.3 ~ j*1
  educalter_7.4 ~ j*1
  educalter_7.5 ~ j*1
  
  educalter_8.1 ~ j*1
  educalter_8.2 ~ j*1
  educalter_8.3 ~ j*1
  educalter_8.4 ~ j*1
  educalter_8.5 ~ j*1
  
  educalter_9.1 ~ j*1
  educalter_9.2 ~ j*1
  educalter_9.3 ~ j*1
  educalter_9.4 ~ j*1
  educalter_9.5 ~ j*1
  
  educalter_10.1 ~ j*1
  educalter_10.2 ~ j*1
  educalter_10.3 ~ j*1
  educalter_10.4 ~ j*1
  educalter_10.5 ~ j*1
  
  educalter_11.1 ~ j*1
  educalter_11.2 ~ j*1
  educalter_11.3 ~ j*1
  educalter_11.4 ~ j*1
  educalter_11.5 ~ j*1
  
  # Free latent means from t = 2 onward. WHAT DID THIJMEN DO IN HIS STUDY??
  Feducalter_8 ~ 1
  Feducalter_9 ~ 1
  Feducalter_10 ~ 1
  Feducalter_11 ~ 1
  
  
  '
  
fit <- lavaan(myModel, data = datalw, missing = 'ML', fixed.x=FALSE, meanstructure = T)
summary(fit, standardized = T)

#> lavaan 0.6-7 ended normally after 34 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of free parameters                         59
#>   Number of equality constraints                    44
#>                                                       
#>                                                   Used       Total
#>   Number of observations                          2493        2575
#>   Number of missing patterns                      1611            
#>                                                                   
#> Model Test User Model:
#>                                                        
#>   Test statistic                              10192.287
#>   Degrees of freedom                                335
#>   P-value (Chi-square)                            0.000
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Observed
#>   Observed information based on                Hessian
#> 
#> Latent Variables:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   Feducalter_7 =~                                                       
#>     educalter_7.1     1.000                               1.501    0.542
#>     educalter_7.2     1.000                               1.501    0.542
#>     educalter_7.3     1.000                               1.501    0.542
#>     educalter_7.4     1.000                               1.501    0.542
#>     educalter_7.5     1.000                               1.501    0.542
#>   Feducalter_8 =~                                                       
#>     educalter_8.1     1.000                               1.457    0.535
#>     educalter_8.2     1.000                               1.457    0.535
#>     educalter_8.3     1.000                               1.457    0.535
#>     educalter_8.4     1.000                               1.457    0.535
#>     educalter_8.5     1.000                               1.457    0.535
#>   Feducalter_9 =~                                                       
#>     educalter_9.1     1.000                               1.468    0.543
#>     educalter_9.2     1.000                               1.468    0.543
#>     educalter_9.3     1.000                               1.468    0.543
#>     educalter_9.4     1.000                               1.468    0.543
#>     educalter_9.5     1.000                               1.468    0.543
#>   Feducalter_10 =~                                                      
#>     educalter_10.1    1.000                               1.473    0.539
#>     educalter_10.2    1.000                               1.473    0.539
#>     educalter_10.3    1.000                               1.473    0.539
#>     educalter_10.4    1.000                               1.473    0.539
#>     educalter_10.5    1.000                               1.473    0.539
#>   Feducalter_11 =~                                                      
#>     educalter_11.1    1.000                               1.453    0.534
#>     educalter_11.2    1.000                               1.453    0.534
#>     educalter_11.3    1.000                               1.453    0.534
#>     educalter_11.4    1.000                               1.453    0.534
#>     educalter_11.5    1.000                               1.453    0.534
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>    .edcltr_7.1 (j)   12.168    0.043  280.218    0.000   12.168    4.397
#>    .edcltr_7.2 (j)   12.168    0.043  280.218    0.000   12.168    4.397
#>    .edcltr_7.3 (j)   12.168    0.043  280.218    0.000   12.168    4.397
#>    .edcltr_7.4 (j)   12.168    0.043  280.218    0.000   12.168    4.397
#>    .edcltr_7.5 (j)   12.168    0.043  280.218    0.000   12.168    4.397
#>    .edcltr_8.1 (j)   12.168    0.043  280.218    0.000   12.168    4.469
#>    .edcltr_8.2 (j)   12.168    0.043  280.218    0.000   12.168    4.469
#>    .edcltr_8.3 (j)   12.168    0.043  280.218    0.000   12.168    4.469
#>    .edcltr_8.4 (j)   12.168    0.043  280.218    0.000   12.168    4.469
#>    .edcltr_8.5 (j)   12.168    0.043  280.218    0.000   12.168    4.469
#>    .edcltr_9.1 (j)   12.168    0.043  280.218    0.000   12.168    4.498
#>    .edcltr_9.2 (j)   12.168    0.043  280.218    0.000   12.168    4.498
#>    .edcltr_9.3 (j)   12.168    0.043  280.218    0.000   12.168    4.498
#>    .edcltr_9.4 (j)   12.168    0.043  280.218    0.000   12.168    4.498
#>    .edcltr_9.5 (j)   12.168    0.043  280.218    0.000   12.168    4.498
#>    .edclt_10.1 (j)   12.168    0.043  280.218    0.000   12.168    4.450
#>    .edclt_10.2 (j)   12.168    0.043  280.218    0.000   12.168    4.450
#>    .edclt_10.3 (j)   12.168    0.043  280.218    0.000   12.168    4.450
#>    .edclt_10.4 (j)   12.168    0.043  280.218    0.000   12.168    4.450
#>    .edclt_10.5 (j)   12.168    0.043  280.218    0.000   12.168    4.450
#>    .edclt_11.1 (j)   12.168    0.043  280.218    0.000   12.168    4.475
#>    .edclt_11.2 (j)   12.168    0.043  280.218    0.000   12.168    4.475
#>    .edclt_11.3 (j)   12.168    0.043  280.218    0.000   12.168    4.475
#>    .edclt_11.4 (j)   12.168    0.043  280.218    0.000   12.168    4.475
#>    .edclt_11.5 (j)   12.168    0.043  280.218    0.000   12.168    4.475
#>     Feducltr_8        0.103    0.062    1.665    0.096    0.070    0.070
#>     Feducltr_9        0.168    0.061    2.739    0.006    0.114    0.114
#>     Fedcltr_10        0.263    0.062    4.245    0.000    0.179    0.179
#>     Fedcltr_11        0.216    0.062    3.461    0.001    0.149    0.149
#>     Feducltr_7        0.000                               0.000    0.000
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     Feducltr_7        2.252    0.125   17.950    0.000    1.000    1.000
#>     Feducltr_8        2.122    0.124   17.108    0.000    1.000    1.000
#>     Feducltr_9        2.154    0.122   17.710    0.000    1.000    1.000
#>     Fedcltr_10        2.169    0.127   17.094    0.000    1.000    1.000
#>     Fedcltr_11        2.111    0.128   16.450    0.000    1.000    1.000
#>    .edcltr_7.1 (e)    5.408    0.107   50.635    0.000    5.408    0.706
#>    .edcltr_7.2 (e)    5.408    0.107   50.635    0.000    5.408    0.706
#>    .edcltr_7.3 (e)    5.408    0.107   50.635    0.000    5.408    0.706
#>    .edcltr_7.4 (e)    5.408    0.107   50.635    0.000    5.408    0.706
#>    .edcltr_7.5 (e)    5.408    0.107   50.635    0.000    5.408    0.706
#>    .edcltr_8.1 (f)    5.292    0.108   48.925    0.000    5.292    0.714
#>    .edcltr_8.2 (f)    5.292    0.108   48.925    0.000    5.292    0.714
#>    .edcltr_8.3 (f)    5.292    0.108   48.925    0.000    5.292    0.714
#>    .edcltr_8.4 (f)    5.292    0.108   48.925    0.000    5.292    0.714
#>    .edcltr_8.5 (f)    5.292    0.108   48.925    0.000    5.292    0.714
#>    .edcltr_9.1 (g)    5.163    0.104   49.724    0.000    5.163    0.706
#>    .edcltr_9.2 (g)    5.163    0.104   49.724    0.000    5.163    0.706
#>    .edcltr_9.3 (g)    5.163    0.104   49.724    0.000    5.163    0.706
#>    .edcltr_9.4 (g)    5.163    0.104   49.724    0.000    5.163    0.706
#>    .edcltr_9.5 (g)    5.163    0.104   49.724    0.000    5.163    0.706
#>    .edclt_10.1 (h)    5.308    0.109   48.626    0.000    5.308    0.710
#>    .edclt_10.2 (h)    5.308    0.109   48.626    0.000    5.308    0.710
#>    .edclt_10.3 (h)    5.308    0.109   48.626    0.000    5.308    0.710
#>    .edclt_10.4 (h)    5.308    0.109   48.626    0.000    5.308    0.710
#>    .edclt_10.5 (h)    5.308    0.109   48.626    0.000    5.308    0.710
#>    .edclt_11.1 (i)    5.281    0.112   47.063    0.000    5.281    0.714
#>    .edclt_11.2 (i)    5.281    0.112   47.063    0.000    5.281    0.714
#>    .edclt_11.3 (i)    5.281    0.112   47.063    0.000    5.281    0.714
#>    .edclt_11.4 (i)    5.281    0.112   47.063    0.000    5.281    0.714
#>    .edclt_11.5 (i)    5.281    0.112   47.063    0.000    5.281    0.714

# 2. extract the predicted values of the cfa and add them to new dataframe data_wide2
datalwb <- data.frame(datalw, predict(fit))

some descriptives

summary(datalwb[, c(79:88)])

#>   Meducalter_7    Meducalter_8    Meducalter_9   Meducalter_10   Meducalter_11    Feducalter_7    
#>  Min.   : 4.00   Min.   : 4.00   Min.   : 4.00   Min.   : 4.00   Min.   : 4.00   Min.   :-5.5179  
#>  1st Qu.:10.50   1st Qu.:10.50   1st Qu.:10.50   1st Qu.:10.50   1st Qu.:10.50   1st Qu.:-0.6444  
#>  Median :12.00   Median :12.00   Median :12.12   Median :12.33   Median :12.30   Median : 0.0000  
#>  Mean   :12.14   Mean   :12.23   Mean   :12.29   Mean   :12.38   Mean   :12.34   Mean   : 0.0000  
#>  3rd Qu.:13.75   3rd Qu.:13.83   3rd Qu.:14.00   3rd Qu.:14.10   3rd Qu.:14.10   3rd Qu.: 0.7646  
#>  Max.   :16.00   Max.   :16.00   Max.   :16.00   Max.   :16.00   Max.   :16.00   Max.   : 2.5885  
#>  NA's   :390     NA's   :505     NA's   :480     NA's   :507     NA's   :582     NA's   :82       
#>   Feducalter_8      Feducalter_9     Feducalter_10     Feducalter_11    
#>  Min.   :-3.6859   Min.   :-3.8445   Min.   :-4.0375   Min.   :-3.9922  
#>  1st Qu.:-0.5473   1st Qu.:-0.5197   1st Qu.:-0.4423   1st Qu.:-0.4647  
#>  Median : 0.1027   Median : 0.1680   Median : 0.2630   Median : 0.2163  
#>  Mean   : 0.1027   Mean   : 0.1680   Mean   : 0.2630   Mean   : 0.2163  
#>  3rd Qu.: 0.7739   3rd Qu.: 0.8871   3rd Qu.: 0.9807   3rd Qu.: 0.8265  
#>  Max.   : 2.5909   Max.   : 2.6446   Max.   : 2.6592   Max.   : 2.6261  
#>  NA's   :82        NA's   :82        NA's   :82        NA's   :82

cor(datalwb[, c(79:88)], use = "pairwise.complete.obs")

#>               Meducalter_7 Meducalter_8 Meducalter_9 Meducalter_10 Meducalter_11 Feducalter_7
#> Meducalter_7     1.0000000    0.6907944    0.7141508     0.6756302     0.6640801    0.9634812
#> Meducalter_8     0.6907944    1.0000000    0.7402949     0.7019350     0.6671828    0.6371311
#> Meducalter_9     0.7141508    0.7402949    1.0000000     0.7293267     0.7112851    0.6656154
#> Meducalter_10    0.6756302    0.7019350    0.7293267     1.0000000     0.7396820    0.6308042
#> Meducalter_11    0.6640801    0.6671828    0.7112851     0.7396820     1.0000000    0.6235384
#> Feducalter_7     0.9634812    0.6371311    0.6656154     0.6308042     0.6235384    1.0000000
#> Feducalter_8     0.6358454    0.9622939    0.6953644     0.6587963     0.6302273    0.6304442
#> Feducalter_9     0.6589070    0.6828941    0.9632233     0.6772381     0.6584166    0.6545687
#> Feducalter_10    0.6193559    0.6556651    0.6776771     0.9599566     0.6900632    0.6152511
#> Feducalter_11    0.5943153    0.6107763    0.6424748     0.6772533     0.9584287    0.5913715
#>               Feducalter_8 Feducalter_9 Feducalter_10 Feducalter_11
#> Meducalter_7     0.6358454    0.6589070     0.6193559     0.5943153
#> Meducalter_8     0.9622939    0.6828941     0.6556651     0.6107763
#> Meducalter_9     0.6953644    0.9632233     0.6776771     0.6424748
#> Meducalter_10    0.6587963    0.6772381     0.9599566     0.6772533
#> Meducalter_11    0.6302273    0.6584166     0.6900632     0.9584287
#> Feducalter_7     0.6304442    0.6545687     0.6152511     0.5913715
#> Feducalter_8     1.0000000    0.6821636     0.6546583     0.6159324
#> Feducalter_9     0.6821636    1.0000000     0.6765447     0.6396061
#> Feducalter_10    0.6546583    0.6765447     1.0000000     0.6781407
#> Feducalter_11    0.6159324    0.6396061     0.6781407     1.0000000

---

Two wave APIM/CLPM

Let us start with some descriptives.

summary(datalw$eu_10)
summary(datalw$eu_11)
summary(datalw$educalter_10.1)
summary(datalw$educalter_11.1)

var(cbind(datalw$eu_10, datalw$eu_11, datalw$educalter_10.1, datalw$educalter_11.1), na.rm = F, use = "pairwise.complete.obs")

#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   0.000   0.000   1.000   1.419   2.000   4.000 
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>   0.000   0.000   2.000   1.512   2.000   4.000 
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
#>     4.0    10.0    11.5    12.4    15.0    16.0     562 
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
#>     4.0    10.0    11.5    12.4    15.0    16.0     629 
#>           [,1]      [,2]      [,3]      [,4]
#> [1,] 1.3709664 0.9892388 0.6068081 0.5765388
#> [2,] 0.9892388 1.4511906 0.6030401 0.6450207
#> [3,] 0.6068081 0.6030401 7.2749276 4.5197169
#> [4,] 0.5765388 0.6450207 4.5197169 7.1008853

APIM

myModel <- "
  # Estimate the lagged effects
  eu_11 + educalter_11.1  ~ eu_10 + educalter_10.1
  
  # Estimate the covariance at the first wave. 
  eu_10 ~~ educalter_10.1 # Covariance

  # Estimate the covariances between the residuals
  eu_11 ~~ educalter_11.1
  
  # Estimate the variance 
  eu_10 ~~ eu_10 
  educalter_10.1 ~~ educalter_10.1
  
  # Estimate the residual variance
  eu_11 ~~ eu_11 
  educalter_11.1 ~~ educalter_11.1
  
  # intercepts
  eu_10 ~ 1
  eu_11 ~ 1
  educalter_10.1 ~ 1
  educalter_11.1 ~ 1
"



fit <- lavaan(myModel, data = datalw, missing = "ML", meanstructure = T)
summary(fit, standardized = T)

#> lavaan 0.6-7 ended normally after 42 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of free parameters                         14
#>                                                       
#>   Number of observations                          2575
#>   Number of missing patterns                         4
#>                                                       
#> Model Test User Model:
#>                                                       
#>   Test statistic                                 0.000
#>   Degrees of freedom                                 0
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Observed
#>   Observed information based on                Hessian
#> 
#> Regressions:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   eu_11 ~                                                               
#>     eu_10             0.711    0.015   48.197    0.000    0.711    0.691
#>     educalter_10.1    0.025    0.007    3.588    0.000    0.025    0.057
#>   educalter_11.1 ~                                                      
#>     eu_10             0.158    0.041    3.839    0.000    0.158    0.069
#>     educalter_10.1    0.624    0.018   34.300    0.000    0.624    0.630
#> 
#> Covariances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   eu_10 ~~                                                              
#>     educalter_10.1    0.597    0.070    8.585    0.000    0.597    0.189
#>  .eu_11 ~~                                                              
#>    .educalter_11.1    0.128    0.041    3.087    0.002    0.128    0.073
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     eu_10             1.419    0.023   61.511    0.000    1.419    1.212
#>    .eu_11             0.192    0.087    2.215    0.027    0.192    0.159
#>     educalter_10.1   12.328    0.059  209.800    0.000   12.328    4.569
#>    .educalter_11.1    4.446    0.227   19.574    0.000    4.446    1.662
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     eu_10             1.370    0.038   35.882    0.000    1.370    1.000
#>     educalter_10.1    7.280    0.228   31.992    0.000    7.280    1.000
#>    .eu_11             0.733    0.020   35.832    0.000    0.733    0.505
#>    .educalter_11.1    4.165    0.139   29.881    0.000    4.165    0.582

---

CLPM

myModel <- "
  # Create within-person centered variables
  weducalter_10.1 =~ 1*educalter_10.1
  weducalter_11.1 =~ 1*educalter_11.1
  weu_10 =~ 1*eu_10
  weu_11 =~ 1*eu_11 
  
  # Estimate the lagged effects
  weu_11 + weducalter_11.1  ~ weu_10 + weducalter_10.1
  
  # Estimate the covariance at the first wave. 
  weu_10 ~~ weducalter_10.1 # Covariance

  # Estimate the covariances between the residuals
  weu_11 ~~ weducalter_11.1
  
  # Estimate the variance 
  weu_10 ~~ weu_10 
  weducalter_10.1 ~~ weducalter_10.1
  
  # Estimate the residual variance
  weu_11 ~~ weu_11 
  weducalter_11.1 ~~ weducalter_11.1
 
"

fit <- lavaan(myModel, data = datalw, missing = "ML", meanstructure = T, int.ov.free = T)
summary(fit, standardized = T)

#> lavaan 0.6-7 ended normally after 42 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of free parameters                         14
#>                                                       
#>   Number of observations                          2575
#>   Number of missing patterns                         4
#>                                                       
#> Model Test User Model:
#>                                                       
#>   Test statistic                                 0.000
#>   Degrees of freedom                                 0
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Observed
#>   Observed information based on                Hessian
#> 
#> Latent Variables:
#>                      Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   weducalter_10.1 =~                                                      
#>     educalter_10.1      1.000                               2.698    1.000
#>   weducalter_11.1 =~                                                      
#>     educalter_11.1      1.000                               2.675    1.000
#>   weu_10 =~                                                               
#>     eu_10               1.000                               1.171    1.000
#>   weu_11 =~                                                               
#>     eu_11               1.000                               1.204    1.000
#> 
#> Regressions:
#>                     Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   weu_11 ~                                                               
#>     weu_10             0.711    0.015   48.197    0.000    0.691    0.691
#>     weducaltr_10.1     0.025    0.007    3.588    0.000    0.057    0.057
#>   weducalter_11.1 ~                                                      
#>     weu_10             0.158    0.041    3.839    0.000    0.069    0.069
#>     weducaltr_10.1     0.624    0.018   34.300    0.000    0.630    0.630
#> 
#> Covariances:
#>                      Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   weducalter_10.1 ~~                                                      
#>     weu_10              0.597    0.070    8.585    0.000    0.189    0.189
#>  .weducalter_11.1 ~~                                                      
#>    .weu_11              0.128    0.041    3.087    0.002    0.073    0.073
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>    .educalter_10.1   12.328    0.059  209.800    0.000   12.328    4.569
#>    .educalter_11.1   12.367    0.059  210.200    0.000   12.367    4.624
#>    .eu_10             1.419    0.023   61.511    0.000    1.419    1.212
#>    .eu_11             1.512    0.024   63.713    0.000    1.512    1.256
#>     weducaltr_10.1    0.000                               0.000    0.000
#>    .weducaltr_11.1    0.000                               0.000    0.000
#>     weu_10            0.000                               0.000    0.000
#>    .weu_11            0.000                               0.000    0.000
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     weu_10            1.370    0.038   35.882    0.000    1.000    1.000
#>     weducaltr_10.1    7.280    0.228   31.992    0.000    1.000    1.000
#>    .weu_11            0.733    0.020   35.832    0.000    0.505    0.505
#>    .weducaltr_11.1    4.165    0.139   29.881    0.000    0.582    0.582
#>    .educalter_10.1    0.000                               0.000    0.000
#>    .educalter_11.1    0.000                               0.000    0.000
#>    .eu_10             0.000                               0.000    0.000
#>    .eu_11             0.000                               0.000    0.000

---

five wave APIM/CLPM

five wave APIM

myModel <- '
  # Estimate the lagged effects (constrained)
  eu_8   ~ a*eu_7 + b*educalter_7.1
  eu_9   ~ a*eu_8 + b*educalter_8.1
  eu_10  ~ a*eu_9 + b*educalter_9.1
  eu_11  ~ a*eu_10 + b*educalter_10.1
  
  educalter_8.1  ~ c*eu_7 + d*educalter_7.1
  educalter_9.1  ~ c*eu_8 + d*educalter_8.1
  educalter_10.1  ~ c*eu_9 + d*educalter_9.1
  educalter_11.1  ~ c*eu_10 + d*educalter_10.1
  
  # Estimate the covariance at the first wave. 
  eu_7 ~~ educalter_7.1 # Covariance

  # Estimate the covariances between the residuals
  eu_8 ~~ educalter_8.1
  eu_9 ~~ educalter_9.1
  eu_10 ~~ educalter_10.1
  eu_11 ~~ educalter_11.1
  
  # Estimate the variance 
  eu_7 ~~ eu_7 
  educalter_7.1 ~~ educalter_7.1
  
  # Estimate the residual variance
  eu_8 ~~ eu_8 
  educalter_8.1 ~~ educalter_8.1
  eu_9 ~~ eu_9 
  educalter_9.1 ~~ educalter_9.1
  eu_10 ~~ eu_10 
  educalter_10.1 ~~ educalter_10.1
  eu_11 ~~ eu_11 
  educalter_11.1 ~~ educalter_11.1
  
  # intercepts
  eu_7 ~ 1
  eu_8 ~ 1
  eu_9 ~ 1
  eu_10 ~ 1
  eu_11 ~ 1
  educalter_7.1 ~ 1
  educalter_8.1 ~ 1
  educalter_9.1 ~ 1
  educalter_10.1 ~ 1
  educalter_11.1 ~ 1
'



fit <- lavaan(myModel, data = datalw, missing = 'ML')
summary(fit, standardized = T)

#> lavaan 0.6-7 ended normally after 41 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of free parameters                         41
#>   Number of equality constraints                    12
#>                                                       
#>   Number of observations                          2575
#>   Number of missing patterns                        32
#>                                                       
#> Model Test User Model:
#>                                                       
#>   Test statistic                              2313.682
#>   Degrees of freedom                                36
#>   P-value (Chi-square)                           0.000
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Observed
#>   Observed information based on                Hessian
#> 
#> Regressions:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   eu_8 ~                                                                
#>     eu_7       (a)    0.697    0.007   95.940    0.000    0.697    0.685
#>     edcltr_7.1 (b)    0.023    0.003    6.613    0.000    0.023    0.051
#>   eu_9 ~                                                                
#>     eu_8       (a)    0.697    0.007   95.940    0.000    0.697    0.697
#>     edcltr_8.1 (b)    0.023    0.003    6.613    0.000    0.023    0.052
#>   eu_10 ~                                                               
#>     eu_9       (a)    0.697    0.007   95.940    0.000    0.697    0.687
#>     edcltr_9.1 (b)    0.023    0.003    6.613    0.000    0.023    0.050
#>   eu_11 ~                                                               
#>     eu_10      (a)    0.697    0.007   95.940    0.000    0.697    0.692
#>     edclt_10.1 (b)    0.023    0.003    6.613    0.000    0.023    0.050
#>   educalter_8.1 ~                                                       
#>     eu_7       (c)    0.197    0.019   10.186    0.000    0.197    0.084
#>     edcltr_7.1 (d)    0.622    0.009   71.419    0.000    0.622    0.614
#>   educalter_9.1 ~                                                       
#>     eu_8       (c)    0.197    0.019   10.186    0.000    0.197    0.087
#>     edcltr_8.1 (d)    0.622    0.009   71.419    0.000    0.622    0.634
#>   educalter_10.1 ~                                                      
#>     eu_9       (c)    0.197    0.019   10.186    0.000    0.197    0.086
#>     edcltr_9.1 (d)    0.622    0.009   71.419    0.000    0.622    0.616
#>   educalter_11.1 ~                                                      
#>     eu_10      (c)    0.197    0.019   10.186    0.000    0.197    0.088
#>     edclt_10.1 (d)    0.622    0.009   71.419    0.000    0.622    0.627
#> 
#> Covariances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   eu_7 ~~                                                               
#>     educalter_7.1     0.592    0.067    8.865    0.000    0.592    0.191
#>  .eu_8 ~~                                                               
#>    .educalter_8.1     0.046    0.040    1.164    0.245    0.046    0.026
#>  .eu_9 ~~                                                               
#>    .educalter_9.1     0.094    0.038    2.505    0.012    0.094    0.056
#>  .eu_10 ~~                                                              
#>    .educalter_10.1    0.049    0.040    1.231    0.218    0.049    0.028
#>  .eu_11 ~~                                                              
#>    .educalter_11.1    0.124    0.041    3.045    0.002    0.124    0.072
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     eu_7              1.263    0.023   55.406    0.000    1.263    1.092
#>    .eu_8              0.172    0.044    3.938    0.000    0.172    0.146
#>    .eu_9              0.072    0.044    1.640    0.101    0.072    0.061
#>    .eu_10             0.258    0.044    5.859    0.000    0.258    0.216
#>    .eu_11             0.246    0.044    5.562    0.000    0.246    0.205
#>     educalter_7.1    12.119    0.057  213.349    0.000   12.119    4.521
#>    .educalter_8.1     4.479    0.114   39.383    0.000    4.479    1.649
#>    .educalter_9.1     4.322    0.114   37.764    0.000    4.322    1.622
#>    .educalter_10.1    4.455    0.114   38.979    0.000    4.455    1.658
#>    .educalter_11.1    4.436    0.115   38.547    0.000    4.436    1.664
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     eu_7              1.338    0.037   35.882    0.000    1.338    1.000
#>     educalter_7.1     7.187    0.219   32.884    0.000    7.187    1.000
#>    .eu_8              0.714    0.020   35.844    0.000    0.714    0.515
#>    .educalter_8.1     4.403    0.142   31.075    0.000    4.403    0.597
#>    .eu_9              0.689    0.019   35.855    0.000    0.689    0.498
#>    .educalter_9.1     4.054    0.131   30.941    0.000    4.054    0.571
#>    .eu_10             0.729    0.020   35.840    0.000    0.729    0.511
#>    .educalter_10.1    4.267    0.138   30.874    0.000    4.267    0.591
#>    .eu_11             0.733    0.020   35.847    0.000    0.733    0.506
#>    .educalter_11.1    4.108    0.136   30.244    0.000    4.108    0.578

five wave CLPM

myModel <- '
  # Estimate the lagged effects (constrained)
  eu_8   ~ a*eu_7 + b*educalter_7.1
  eu_9   ~ a*eu_8 + b*educalter_8.1
  eu_10  ~ a*eu_9 + b*educalter_9.1
  eu_11  ~ a*eu_10 + b*educalter_10.1
  
  educalter_8.1  ~ c*eu_7 + d*educalter_7.1
  educalter_9.1  ~ c*eu_8 + d*educalter_8.1
  educalter_10.1  ~ c*eu_9 + d*educalter_9.1
  educalter_11.1  ~ c*eu_10 + d*educalter_10.1
  
  # Estimate the covariance at the first wave. 
  eu_7 ~~ educalter_7.1 # Covariance

  # Estimate the covariances between the residuals
  eu_8 ~~ educalter_8.1
  eu_9 ~~ educalter_9.1
  eu_10 ~~ educalter_10.1
  eu_11 ~~ educalter_11.1
  
  # Estimate the variance 
  eu_7 ~~ eu_7 
  educalter_7.1 ~~ educalter_7.1
  
  # Estimate the residual variance
  eu_8 ~~ eu_8 
  educalter_8.1 ~~ educalter_8.1
  eu_9 ~~ eu_9 
  educalter_9.1 ~~ educalter_9.1
  eu_10 ~~ eu_10 
  educalter_10.1 ~~ educalter_10.1
  eu_11 ~~ eu_11 
  educalter_11.1 ~~ educalter_11.1
  
  # intercepts
  eu_7 ~ 1
  eu_8 ~ 1
  eu_9 ~ 1
  eu_10 ~ 1
  eu_11 ~ 1
  
  educalter_7.1 ~ 1
   educalter_8.1 ~ 1
    educalter_9.1 ~ 1
     educalter_10.1 ~ 1
      educalter_11.1 ~ 1
  
'



fit <- lavaan(myModel, data = datalw, missing = 'ML', meanstructure = T, int.ov.free = T)
summary(fit, standardized = T)

#> lavaan 0.6-7 ended normally after 41 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of free parameters                         41
#>   Number of equality constraints                    12
#>                                                       
#>   Number of observations                          2575
#>   Number of missing patterns                        32
#>                                                       
#> Model Test User Model:
#>                                                       
#>   Test statistic                              2313.682
#>   Degrees of freedom                                36
#>   P-value (Chi-square)                           0.000
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Observed
#>   Observed information based on                Hessian
#> 
#> Regressions:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   eu_8 ~                                                                
#>     eu_7       (a)    0.697    0.007   95.940    0.000    0.697    0.685
#>     edcltr_7.1 (b)    0.023    0.003    6.613    0.000    0.023    0.051
#>   eu_9 ~                                                                
#>     eu_8       (a)    0.697    0.007   95.940    0.000    0.697    0.697
#>     edcltr_8.1 (b)    0.023    0.003    6.613    0.000    0.023    0.052
#>   eu_10 ~                                                               
#>     eu_9       (a)    0.697    0.007   95.940    0.000    0.697    0.687
#>     edcltr_9.1 (b)    0.023    0.003    6.613    0.000    0.023    0.050
#>   eu_11 ~                                                               
#>     eu_10      (a)    0.697    0.007   95.940    0.000    0.697    0.692
#>     edclt_10.1 (b)    0.023    0.003    6.613    0.000    0.023    0.050
#>   educalter_8.1 ~                                                       
#>     eu_7       (c)    0.197    0.019   10.186    0.000    0.197    0.084
#>     edcltr_7.1 (d)    0.622    0.009   71.419    0.000    0.622    0.614
#>   educalter_9.1 ~                                                       
#>     eu_8       (c)    0.197    0.019   10.186    0.000    0.197    0.087
#>     edcltr_8.1 (d)    0.622    0.009   71.419    0.000    0.622    0.634
#>   educalter_10.1 ~                                                      
#>     eu_9       (c)    0.197    0.019   10.186    0.000    0.197    0.086
#>     edcltr_9.1 (d)    0.622    0.009   71.419    0.000    0.622    0.616
#>   educalter_11.1 ~                                                      
#>     eu_10      (c)    0.197    0.019   10.186    0.000    0.197    0.088
#>     edclt_10.1 (d)    0.622    0.009   71.419    0.000    0.622    0.627
#> 
#> Covariances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   eu_7 ~~                                                               
#>     educalter_7.1     0.592    0.067    8.865    0.000    0.592    0.191
#>  .eu_8 ~~                                                               
#>    .educalter_8.1     0.046    0.040    1.164    0.245    0.046    0.026
#>  .eu_9 ~~                                                               
#>    .educalter_9.1     0.094    0.038    2.505    0.012    0.094    0.056
#>  .eu_10 ~~                                                              
#>    .educalter_10.1    0.049    0.040    1.231    0.218    0.049    0.028
#>  .eu_11 ~~                                                              
#>    .educalter_11.1    0.124    0.041    3.045    0.002    0.124    0.072
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     eu_7              1.263    0.023   55.406    0.000    1.263    1.092
#>    .eu_8              0.172    0.044    3.938    0.000    0.172    0.146
#>    .eu_9              0.072    0.044    1.640    0.101    0.072    0.061
#>    .eu_10             0.258    0.044    5.859    0.000    0.258    0.216
#>    .eu_11             0.246    0.044    5.562    0.000    0.246    0.205
#>     educalter_7.1    12.119    0.057  213.349    0.000   12.119    4.521
#>    .educalter_8.1     4.479    0.114   39.383    0.000    4.479    1.649
#>    .educalter_9.1     4.322    0.114   37.764    0.000    4.322    1.622
#>    .educalter_10.1    4.455    0.114   38.979    0.000    4.455    1.658
#>    .educalter_11.1    4.436    0.115   38.547    0.000    4.436    1.664
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     eu_7              1.338    0.037   35.882    0.000    1.338    1.000
#>     educalter_7.1     7.187    0.219   32.884    0.000    7.187    1.000
#>    .eu_8              0.714    0.020   35.844    0.000    0.714    0.515
#>    .educalter_8.1     4.403    0.142   31.075    0.000    4.403    0.597
#>    .eu_9              0.689    0.019   35.855    0.000    0.689    0.498
#>    .educalter_9.1     4.054    0.131   30.941    0.000    4.054    0.571
#>    .eu_10             0.729    0.020   35.840    0.000    0.729    0.511
#>    .educalter_10.1    4.267    0.138   30.874    0.000    4.267    0.591
#>    .eu_11             0.733    0.020   35.847    0.000    0.733    0.506
#>    .educalter_11.1    4.108    0.136   30.244    0.000    4.108    0.578

---

five wave CLPM vs RI-CLPM

five wave CLPM

myModel <- '
  # Estimate the lagged effects (constrained)
  eu_8   ~ a*eu_7 + b*educalter_7.1
  eu_9   ~ a*eu_8 + b*educalter_8.1
  eu_10  ~ a*eu_9 + b*educalter_9.1
  eu_11  ~ a*eu_10 + b*educalter_10.1
  
  educalter_8.1  ~ c*eu_7 + d*educalter_7.1
  educalter_9.1  ~ c*eu_8 + d*educalter_8.1
  educalter_10.1  ~ c*eu_9 + d*educalter_9.1
  educalter_11.1  ~ c*eu_10 + d*educalter_10.1
  
  # Estimate the covariance at the first wave. 
  eu_7 ~~ educalter_7.1 # Covariance

  # Estimate the covariances between the residuals
  eu_8 ~~ educalter_8.1
  eu_9 ~~ educalter_9.1
  eu_10 ~~ educalter_10.1
  eu_11 ~~ educalter_11.1
  
  # Estimate the variance 
  eu_7 ~~ eu_7 
  educalter_7.1 ~~ educalter_7.1
  
  # Estimate the residual variance
  eu_8 ~~ eu_8 
  educalter_8.1 ~~ educalter_8.1
  eu_9 ~~ eu_9 
  educalter_9.1 ~~ educalter_9.1
  eu_10 ~~ eu_10 
  educalter_10.1 ~~ educalter_10.1
  eu_11 ~~ eu_11 
  educalter_11.1 ~~ educalter_11.1
  
  # intercepts
  eu_7 ~ 1
  eu_8 ~ 1
  eu_9 ~ 1
  eu_10 ~ 1
  eu_11 ~ 1
  
  educalter_7.1 ~ 1
   educalter_8.1 ~ 1
    educalter_9.1 ~ 1
     educalter_10.1 ~ 1
      educalter_11.1 ~ 1
  
'



fit <- lavaan(myModel, data = datalw, missing = 'ML', meanstructure = T, int.ov.free = T)
summary(fit, standardized = T)

#> lavaan 0.6-7 ended normally after 41 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of free parameters                         41
#>   Number of equality constraints                    12
#>                                                       
#>   Number of observations                          2575
#>   Number of missing patterns                        32
#>                                                       
#> Model Test User Model:
#>                                                       
#>   Test statistic                              2313.682
#>   Degrees of freedom                                36
#>   P-value (Chi-square)                           0.000
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Observed
#>   Observed information based on                Hessian
#> 
#> Regressions:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   eu_8 ~                                                                
#>     eu_7       (a)    0.697    0.007   95.940    0.000    0.697    0.685
#>     edcltr_7.1 (b)    0.023    0.003    6.613    0.000    0.023    0.051
#>   eu_9 ~                                                                
#>     eu_8       (a)    0.697    0.007   95.940    0.000    0.697    0.697
#>     edcltr_8.1 (b)    0.023    0.003    6.613    0.000    0.023    0.052
#>   eu_10 ~                                                               
#>     eu_9       (a)    0.697    0.007   95.940    0.000    0.697    0.687
#>     edcltr_9.1 (b)    0.023    0.003    6.613    0.000    0.023    0.050
#>   eu_11 ~                                                               
#>     eu_10      (a)    0.697    0.007   95.940    0.000    0.697    0.692
#>     edclt_10.1 (b)    0.023    0.003    6.613    0.000    0.023    0.050
#>   educalter_8.1 ~                                                       
#>     eu_7       (c)    0.197    0.019   10.186    0.000    0.197    0.084
#>     edcltr_7.1 (d)    0.622    0.009   71.419    0.000    0.622    0.614
#>   educalter_9.1 ~                                                       
#>     eu_8       (c)    0.197    0.019   10.186    0.000    0.197    0.087
#>     edcltr_8.1 (d)    0.622    0.009   71.419    0.000    0.622    0.634
#>   educalter_10.1 ~                                                      
#>     eu_9       (c)    0.197    0.019   10.186    0.000    0.197    0.086
#>     edcltr_9.1 (d)    0.622    0.009   71.419    0.000    0.622    0.616
#>   educalter_11.1 ~                                                      
#>     eu_10      (c)    0.197    0.019   10.186    0.000    0.197    0.088
#>     edclt_10.1 (d)    0.622    0.009   71.419    0.000    0.622    0.627
#> 
#> Covariances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   eu_7 ~~                                                               
#>     educalter_7.1     0.592    0.067    8.865    0.000    0.592    0.191
#>  .eu_8 ~~                                                               
#>    .educalter_8.1     0.046    0.040    1.164    0.245    0.046    0.026
#>  .eu_9 ~~                                                               
#>    .educalter_9.1     0.094    0.038    2.505    0.012    0.094    0.056
#>  .eu_10 ~~                                                              
#>    .educalter_10.1    0.049    0.040    1.231    0.218    0.049    0.028
#>  .eu_11 ~~                                                              
#>    .educalter_11.1    0.124    0.041    3.045    0.002    0.124    0.072
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     eu_7              1.263    0.023   55.406    0.000    1.263    1.092
#>    .eu_8              0.172    0.044    3.938    0.000    0.172    0.146
#>    .eu_9              0.072    0.044    1.640    0.101    0.072    0.061
#>    .eu_10             0.258    0.044    5.859    0.000    0.258    0.216
#>    .eu_11             0.246    0.044    5.562    0.000    0.246    0.205
#>     educalter_7.1    12.119    0.057  213.349    0.000   12.119    4.521
#>    .educalter_8.1     4.479    0.114   39.383    0.000    4.479    1.649
#>    .educalter_9.1     4.322    0.114   37.764    0.000    4.322    1.622
#>    .educalter_10.1    4.455    0.114   38.979    0.000    4.455    1.658
#>    .educalter_11.1    4.436    0.115   38.547    0.000    4.436    1.664
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     eu_7              1.338    0.037   35.882    0.000    1.338    1.000
#>     educalter_7.1     7.187    0.219   32.884    0.000    7.187    1.000
#>    .eu_8              0.714    0.020   35.844    0.000    0.714    0.515
#>    .educalter_8.1     4.403    0.142   31.075    0.000    4.403    0.597
#>    .eu_9              0.689    0.019   35.855    0.000    0.689    0.498
#>    .educalter_9.1     4.054    0.131   30.941    0.000    4.054    0.571
#>    .eu_10             0.729    0.020   35.840    0.000    0.729    0.511
#>    .educalter_10.1    4.267    0.138   30.874    0.000    4.267    0.591
#>    .eu_11             0.733    0.020   35.847    0.000    0.733    0.506
#>    .educalter_11.1    4.108    0.136   30.244    0.000    4.108    0.578

---

five wave RI-CLPM

myModel <- '
 # Create between components (random intercepts)
  RIx =~ 1*educalter_7.1 + 1*educalter_8.1 + 1*educalter_9.1 + 1*educalter_10.1 + 1*educalter_11.1
  RIy =~ 1*eu_7 + 1*eu_8 + 1*eu_9 + 1*eu_10 + 1*eu_11


   # Create within-person centered variables
  weducalter_7.1 =~ 1*educalter_7.1
  weducalter_8.1 =~ 1*educalter_8.1
  weducalter_9.1 =~ 1*educalter_9.1
  weducalter_10.1 =~ 1*educalter_10.1
  weducalter_11.1 =~ 1*educalter_11.1
  weu_7 =~ 1*eu_7
  weu_8 =~ 1*eu_8
  weu_9 =~ 1*eu_9
  weu_10 =~ 1*eu_10
  weu_11 =~ 1*eu_11 
  
  # Estimate the lagged effects (constrained)
  weu_8   ~ a*weu_7 + b*weducalter_7.1
  weu_9   ~ a*weu_8 + b*weducalter_8.1
  weu_10  ~ a*weu_9 + b*weducalter_9.1
  weu_11  ~ a*weu_10 + b*weducalter_10.1
  
  weducalter_8.1  ~ c*weu_7 + d*weducalter_7.1
  weducalter_9.1  ~ c*weu_8 + d*weducalter_8.1
  weducalter_10.1  ~ c*weu_9 + d*weducalter_9.1
  weducalter_11.1  ~ c*weu_10 + d*weducalter_10.1
  
  # Estimate the covariance at the first wave. WITHIN
  weu_7 ~~ weducalter_7.1 # Covariance

  # Estimate the covariances between the residuals. WITHIN
  weu_8 ~~ weducalter_8.1
  weu_9 ~~ weducalter_9.1
  weu_10 ~~ weducalter_10.1
  weu_11 ~~ weducalter_11.1
  
   # Estimate the variance and covariance of the random intercepts. BETWEEN
  RIx ~~ RIx
  RIy ~~ RIy
  RIx ~~ RIy
  
  # Estimate the variance. WITHIN
  weu_7 ~~ weu_7 
  weducalter_7.1 ~~ weducalter_7.1
  
  # Estimate the residual variance. WITHIN
  weu_8 ~~ weu_8 
  weducalter_8.1 ~~ weducalter_8.1
  weu_9 ~~ weu_9 
  weducalter_9.1 ~~ weducalter_9.1
  weu_10 ~~ weu_10 
  weducalter_10.1 ~~ weducalter_10.1
  weu_11 ~~ weu_11 
  weducalter_11.1 ~~ weducalter_11.1
  
'



fit <- lavaan(myModel, data = datalw, missing = 'ML', meanstructure = T, int.ov.free = T)
summary(fit, standardized = T)

#> lavaan 0.6-7 ended normally after 74 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of free parameters                         44
#>   Number of equality constraints                    12
#>                                                       
#>   Number of observations                          2575
#>   Number of missing patterns                        32
#>                                                       
#> Model Test User Model:
#>                                                       
#>   Test statistic                                52.852
#>   Degrees of freedom                                33
#>   P-value (Chi-square)                           0.016
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Observed
#>   Observed information based on                Hessian
#> 
#> Latent Variables:
#>                      Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   RIx =~                                                                  
#>     educalter_7.1       1.000                               2.074    0.766
#>     educalter_8.1       1.000                               2.074    0.776
#>     educalter_9.1       1.000                               2.074    0.786
#>     educalter_10.1      1.000                               2.074    0.774
#>     educalter_11.1      1.000                               2.074    0.780
#>   RIy =~                                                                  
#>     eu_7                1.000                               0.954    0.814
#>     eu_8                1.000                               0.954    0.809
#>     eu_9                1.000                               0.954    0.811
#>     eu_10               1.000                               0.954    0.805
#>     eu_11               1.000                               0.954    0.800
#>   weducalter_7.1 =~                                                       
#>     educalter_7.1       1.000                               1.741    0.643
#>   weducalter_8.1 =~                                                       
#>     educalter_8.1       1.000                               1.685    0.630
#>   weducalter_9.1 =~                                                       
#>     educalter_9.1       1.000                               1.633    0.619
#>   weducalter_10.1 =~                                                      
#>     educalter_10.1      1.000                               1.695    0.633
#>   weducalter_11.1 =~                                                      
#>     educalter_11.1      1.000                               1.664    0.626
#>   weu_7 =~                                                                
#>     eu_7                1.000                               0.681    0.581
#>   weu_8 =~                                                                
#>     eu_8                1.000                               0.694    0.588
#>   weu_9 =~                                                                
#>     eu_9                1.000                               0.689    0.585
#>   weu_10 =~                                                               
#>     eu_10               1.000                               0.703    0.593
#>   weu_11 =~                                                               
#>     eu_11               1.000                               0.716    0.600
#> 
#> Regressions:
#>                     Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   weu_8 ~                                                                
#>     weu_7      (a)     0.135    0.015    8.836    0.000    0.133    0.133
#>     wdcltr_7.1 (b)     0.002    0.006    0.318    0.751    0.005    0.005
#>   weu_9 ~                                                                
#>     weu_8      (a)     0.135    0.015    8.836    0.000    0.136    0.136
#>     wdcltr_8.1 (b)     0.002    0.006    0.318    0.751    0.005    0.005
#>   weu_10 ~                                                               
#>     weu_9      (a)     0.135    0.015    8.836    0.000    0.133    0.133
#>     wdcltr_9.1 (b)     0.002    0.006    0.318    0.751    0.004    0.004
#>   weu_11 ~                                                               
#>     weu_10     (a)     0.135    0.015    8.836    0.000    0.133    0.133
#>     wdclt_10.1 (b)     0.002    0.006    0.318    0.751    0.004    0.004
#>   weducalter_8.1 ~                                                       
#>     weu_7      (c)     0.065    0.036    1.797    0.072    0.026    0.026
#>     wdcltr_7.1 (d)     0.048    0.018    2.693    0.007    0.049    0.049
#>   weducalter_9.1 ~                                                       
#>     weu_8      (c)     0.065    0.036    1.797    0.072    0.028    0.028
#>     wdcltr_8.1 (d)     0.048    0.018    2.693    0.007    0.049    0.049
#>   weducalter_10.1 ~                                                      
#>     weu_9      (c)     0.065    0.036    1.797    0.072    0.026    0.026
#>     wdcltr_9.1 (d)     0.048    0.018    2.693    0.007    0.046    0.046
#>   weducalter_11.1 ~                                                      
#>     weu_10     (c)     0.065    0.036    1.797    0.072    0.027    0.027
#>     wdclt_10.1 (d)     0.048    0.018    2.693    0.007    0.049    0.049
#> 
#> Covariances:
#>                      Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   weducalter_7.1 ~~                                                       
#>     weu_7              -0.020    0.033   -0.592    0.554   -0.017   -0.017
#>  .weducalter_8.1 ~~                                                       
#>    .weu_8               0.045    0.033    1.349    0.177    0.039    0.039
#>  .weducalter_9.1 ~~                                                       
#>    .weu_9               0.024    0.032    0.755    0.450    0.021    0.021
#>  .weducalter_10.1 ~~                                                      
#>    .weu_10              0.018    0.034    0.523    0.601    0.015    0.015
#>  .weducalter_11.1 ~~                                                      
#>    .weu_11              0.054    0.033    1.629    0.103    0.046    0.046
#>   RIx ~~                                                                  
#>     RIy                 0.595    0.048   12.355    0.000    0.301    0.301
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>    .educalter_7.1    12.097    0.057  213.217    0.000   12.097    4.467
#>    .educalter_8.1    12.254    0.057  216.078    0.000   12.254    4.586
#>    .educalter_9.1    12.218    0.056  219.048    0.000   12.218    4.628
#>    .educalter_10.1   12.293    0.057  215.753    0.000   12.293    4.589
#>    .educalter_11.1   12.339    0.057  216.172    0.000   12.339    4.640
#>    .eu_7              1.263    0.023   54.687    0.000    1.263    1.078
#>    .eu_8              1.325    0.023   57.015    0.000    1.325    1.124
#>    .eu_9              1.272    0.023   54.873    0.000    1.272    1.081
#>    .eu_10             1.419    0.023   60.791    0.000    1.419    1.198
#>    .eu_11             1.512    0.023   64.360    0.000    1.512    1.268
#>     RIx               0.000                               0.000    0.000
#>     RIy               0.000                               0.000    0.000
#>     weducalter_7.1    0.000                               0.000    0.000
#>    .weducalter_8.1    0.000                               0.000    0.000
#>    .weducalter_9.1    0.000                               0.000    0.000
#>    .weducaltr_10.1    0.000                               0.000    0.000
#>    .weducaltr_11.1    0.000                               0.000    0.000
#>     weu_7             0.000                               0.000    0.000
#>    .weu_8             0.000                               0.000    0.000
#>    .weu_9             0.000                               0.000    0.000
#>    .weu_10            0.000                               0.000    0.000
#>    .weu_11            0.000                               0.000    0.000
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     RIx               4.302    0.148   29.067    0.000    1.000    1.000
#>     RIy               0.909    0.029   31.345    0.000    1.000    1.000
#>     weu_7             0.464    0.017   27.552    0.000    1.000    1.000
#>     weducalter_7.1    3.030    0.119   25.541    0.000    1.000    1.000
#>    .weu_8             0.473    0.017   28.236    0.000    0.982    0.982
#>    .weducalter_8.1    2.829    0.117   24.208    0.000    0.997    0.997
#>    .weu_9             0.465    0.016   28.595    0.000    0.981    0.981
#>    .weducalter_9.1    2.658    0.110   24.230    0.000    0.997    0.997
#>    .weu_10            0.485    0.017   28.654    0.000    0.982    0.982
#>    .weducaltr_10.1    2.866    0.117   24.408    0.000    0.997    0.997
#>    .weu_11            0.503    0.017   30.141    0.000    0.982    0.982
#>    .weducaltr_11.1    2.761    0.111   24.828    0.000    0.997    0.997
#>    .educalter_7.1     0.000                               0.000    0.000
#>    .educalter_8.1     0.000                               0.000    0.000
#>    .educalter_9.1     0.000                               0.000    0.000
#>    .educalter_10.1    0.000                               0.000    0.000
#>    .educalter_11.1    0.000                               0.000    0.000
#>    .eu_7              0.000                               0.000    0.000
#>    .eu_8              0.000                               0.000    0.000
#>    .eu_9              0.000                               0.000    0.000
#>    .eu_10             0.000                               0.000    0.000
#>    .eu_11             0.000                               0.000    0.000

---

five wave CLPM one indicator vs CLPM indicators five indactors (one step and two-step) vs aggregation method

five wave CLPM one indicator

myModel <- '
  # Estimate the lagged effects (constrained)
  eu_8   ~ a*eu_7 + b*educalter_7.1
  eu_9   ~ a*eu_8 + b*educalter_8.1
  eu_10  ~ a*eu_9 + b*educalter_9.1
  eu_11  ~ a*eu_10 + b*educalter_10.1
  
  educalter_8.1  ~ c*eu_7 + d*educalter_7.1
  educalter_9.1  ~ c*eu_8 + d*educalter_8.1
  educalter_10.1  ~ c*eu_9 + d*educalter_9.1
  educalter_11.1  ~ c*eu_10 + d*educalter_10.1
  
  # Estimate the covariance at the first wave. 
  eu_7 ~~ educalter_7.1 # Covariance

  # Estimate the covariances between the residuals
  eu_8 ~~ educalter_8.1
  eu_9 ~~ educalter_9.1
  eu_10 ~~ educalter_10.1
  eu_11 ~~ educalter_11.1
  
  # Estimate the variance 
  eu_7 ~~ eu_7 
  educalter_7.1 ~~ educalter_7.1
  
  # Estimate the residual variance
  eu_8 ~~ eu_8 
  educalter_8.1 ~~ educalter_8.1
  eu_9 ~~ eu_9 
  educalter_9.1 ~~ educalter_9.1
  eu_10 ~~ eu_10 
  educalter_10.1 ~~ educalter_10.1
  eu_11 ~~ eu_11 
  educalter_11.1 ~~ educalter_11.1
  
  # intercepts
  eu_7 ~ 1
  eu_8 ~ 1
  eu_9 ~ 1
  eu_10 ~ 1
  eu_11 ~ 1
  
  educalter_7.1 ~ 1
   educalter_8.1 ~ 1
    educalter_9.1 ~ 1
     educalter_10.1 ~ 1
      educalter_11.1 ~ 1
  
'



fit <- lavaan(myModel, data = datalw, missing = 'ML', meanstructure = T, int.ov.free = T)
summary(fit, standardized = T)

#> lavaan 0.6-7 ended normally after 41 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of free parameters                         41
#>   Number of equality constraints                    12
#>                                                       
#>   Number of observations                          2575
#>   Number of missing patterns                        32
#>                                                       
#> Model Test User Model:
#>                                                       
#>   Test statistic                              2313.682
#>   Degrees of freedom                                36
#>   P-value (Chi-square)                           0.000
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Observed
#>   Observed information based on                Hessian
#> 
#> Regressions:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   eu_8 ~                                                                
#>     eu_7       (a)    0.697    0.007   95.940    0.000    0.697    0.685
#>     edcltr_7.1 (b)    0.023    0.003    6.613    0.000    0.023    0.051
#>   eu_9 ~                                                                
#>     eu_8       (a)    0.697    0.007   95.940    0.000    0.697    0.697
#>     edcltr_8.1 (b)    0.023    0.003    6.613    0.000    0.023    0.052
#>   eu_10 ~                                                               
#>     eu_9       (a)    0.697    0.007   95.940    0.000    0.697    0.687
#>     edcltr_9.1 (b)    0.023    0.003    6.613    0.000    0.023    0.050
#>   eu_11 ~                                                               
#>     eu_10      (a)    0.697    0.007   95.940    0.000    0.697    0.692
#>     edclt_10.1 (b)    0.023    0.003    6.613    0.000    0.023    0.050
#>   educalter_8.1 ~                                                       
#>     eu_7       (c)    0.197    0.019   10.186    0.000    0.197    0.084
#>     edcltr_7.1 (d)    0.622    0.009   71.419    0.000    0.622    0.614
#>   educalter_9.1 ~                                                       
#>     eu_8       (c)    0.197    0.019   10.186    0.000    0.197    0.087
#>     edcltr_8.1 (d)    0.622    0.009   71.419    0.000    0.622    0.634
#>   educalter_10.1 ~                                                      
#>     eu_9       (c)    0.197    0.019   10.186    0.000    0.197    0.086
#>     edcltr_9.1 (d)    0.622    0.009   71.419    0.000    0.622    0.616
#>   educalter_11.1 ~                                                      
#>     eu_10      (c)    0.197    0.019   10.186    0.000    0.197    0.088
#>     edclt_10.1 (d)    0.622    0.009   71.419    0.000    0.622    0.627
#> 
#> Covariances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   eu_7 ~~                                                               
#>     educalter_7.1     0.592    0.067    8.865    0.000    0.592    0.191
#>  .eu_8 ~~                                                               
#>    .educalter_8.1     0.046    0.040    1.164    0.245    0.046    0.026
#>  .eu_9 ~~                                                               
#>    .educalter_9.1     0.094    0.038    2.505    0.012    0.094    0.056
#>  .eu_10 ~~                                                              
#>    .educalter_10.1    0.049    0.040    1.231    0.218    0.049    0.028
#>  .eu_11 ~~                                                              
#>    .educalter_11.1    0.124    0.041    3.045    0.002    0.124    0.072
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     eu_7              1.263    0.023   55.406    0.000    1.263    1.092
#>    .eu_8              0.172    0.044    3.938    0.000    0.172    0.146
#>    .eu_9              0.072    0.044    1.640    0.101    0.072    0.061
#>    .eu_10             0.258    0.044    5.859    0.000    0.258    0.216
#>    .eu_11             0.246    0.044    5.562    0.000    0.246    0.205
#>     educalter_7.1    12.119    0.057  213.349    0.000   12.119    4.521
#>    .educalter_8.1     4.479    0.114   39.383    0.000    4.479    1.649
#>    .educalter_9.1     4.322    0.114   37.764    0.000    4.322    1.622
#>    .educalter_10.1    4.455    0.114   38.979    0.000    4.455    1.658
#>    .educalter_11.1    4.436    0.115   38.547    0.000    4.436    1.664
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     eu_7              1.338    0.037   35.882    0.000    1.338    1.000
#>     educalter_7.1     7.187    0.219   32.884    0.000    7.187    1.000
#>    .eu_8              0.714    0.020   35.844    0.000    0.714    0.515
#>    .educalter_8.1     4.403    0.142   31.075    0.000    4.403    0.597
#>    .eu_9              0.689    0.019   35.855    0.000    0.689    0.498
#>    .educalter_9.1     4.054    0.131   30.941    0.000    4.054    0.571
#>    .eu_10             0.729    0.020   35.840    0.000    0.729    0.511
#>    .educalter_10.1    4.267    0.138   30.874    0.000    4.267    0.591
#>    .eu_11             0.733    0.020   35.847    0.000    0.733    0.506
#>    .educalter_11.1    4.108    0.136   30.244    0.000    4.108    0.578

---

five wave CLPM five indicators one-step

myModel <- '
   # Create LATENT variables
  Feducalter_7 =~ 1*educalter_7.1 + 1*educalter_7.2 + 1*educalter_7.3 +  1*educalter_7.4 + 1*educalter_7.5
  Feducalter_8 =~ 1*educalter_8.1 + 1*educalter_8.2 + 1*educalter_8.3 +  1*educalter_8.4 + 1*educalter_8.5
  Feducalter_9 =~ 1*educalter_9.1 + 1*educalter_9.2 + 1*educalter_9.3 +  1*educalter_9.4 + 1*educalter_9.5
  Feducalter_10 =~ 1*educalter_10.1 + 1*educalter_10.2 + 1*educalter_10.3 +  1*educalter_10.4 + 1*educalter_10.5
  Feducalter_11 =~ 1*educalter_11.1 + 1*educalter_11.2 + 1*educalter_11.3 +  1*educalter_11.4 + 1*educalter_11.5
  
  # Free latent means from t = 2 onward. WHAT DID THIJMEN DO IN HIS STUDY?? aND DOES THIS MATTER? 
  Feducalter_8 ~ 1
  Feducalter_9 ~ 1
  Feducalter_10 ~ 1
  Feducalter_11 ~ 1
  
  # Estimate the lagged effects (constrained)
  eu_8   ~ a*eu_7 + b*Feducalter_7
  eu_9   ~ a*eu_8 + b*Feducalter_8
  eu_10  ~ a*eu_9 + b*Feducalter_9
  eu_11  ~ a*eu_10 + b*Feducalter_10
  
  Feducalter_8  ~ c*eu_7 + d*Feducalter_7
  Feducalter_9  ~ c*eu_8 + d*Feducalter_8
  Feducalter_10  ~ c*eu_9 + d*Feducalter_9
  Feducalter_11  ~ c*eu_10 + d*Feducalter_10
  
  # Estimate the covariance at the first wave. 
  eu_7 ~~ Feducalter_7 # Covariance

  # Estimate the covariances between the residuals
  eu_8 ~~ Feducalter_8
  eu_9 ~~ Feducalter_9
  eu_10 ~~ Feducalter_10
  eu_11 ~~ Feducalter_11
  
  # Estimate the variance 
   
  educalter_7.1 ~~ e*educalter_7.1
  educalter_7.2 ~~ e*educalter_7.2
  educalter_7.3 ~~ e*educalter_7.3
  educalter_7.4 ~~ e*educalter_7.4
  educalter_7.5 ~~ e*educalter_7.5
  
  educalter_8.1 ~~ f*educalter_8.1
  educalter_8.2 ~~ f*educalter_8.2
  educalter_8.3 ~~ f*educalter_8.3
  educalter_8.4 ~~ f*educalter_8.4
  educalter_8.5 ~~ f*educalter_8.5
  
  educalter_9.1 ~~ g*educalter_9.1
  educalter_9.2 ~~ g*educalter_9.2
  educalter_9.3 ~~ g*educalter_9.3
  educalter_9.4 ~~ g*educalter_9.4
  educalter_9.5 ~~ g*educalter_9.5
  
  educalter_10.1 ~~ h*educalter_10.1
  educalter_10.2 ~~ h*educalter_10.2
  educalter_10.3 ~~ h*educalter_10.3
  educalter_10.4 ~~ h*educalter_10.4
  educalter_10.5 ~~ h*educalter_10.5
  
  educalter_11.1 ~~ i*educalter_11.1
  educalter_11.2 ~~ i*educalter_11.2
  educalter_11.3 ~~ i*educalter_11.3
  educalter_11.4 ~~ i*educalter_11.4
  educalter_11.5 ~~ i*educalter_11.5
  
  
  
  
  # Estimate the (residual) variance
  eu_7 ~~ eu_7
  eu_8 ~~ eu_8 
  eu_9 ~~ eu_9 
  eu_10 ~~ eu_10 
  eu_11 ~~ eu_11 
  
  Feducalter_7 ~~ Feducalter_7
  Feducalter_8 ~~ Feducalter_8
  Feducalter_9 ~~ Feducalter_9
  Feducalter_10 ~~ Feducalter_10
  Feducalter_11 ~~ Feducalter_11
  
  
  # intercepts
  eu_7 ~ 1
  eu_8 ~ 1
  eu_9 ~ 1
  eu_10 ~ 1
  eu_11 ~ 1
  
  #constrained intercepts
  educalter_7.1 ~ j*1
  educalter_7.2 ~ j*1
  educalter_7.3 ~ j*1
  educalter_7.4 ~ j*1
  educalter_7.5 ~ j*1
  
  educalter_8.1 ~ j*1
  educalter_8.2 ~ j*1
  educalter_8.3 ~ j*1
  educalter_8.4 ~ j*1
  educalter_8.5 ~ j*1
  
  educalter_9.1 ~ j*1
  educalter_9.2 ~ j*1
  educalter_9.3 ~ j*1
  educalter_9.4 ~ j*1
  educalter_9.5 ~ j*1
  
  educalter_10.1 ~ j*1
  educalter_10.2 ~ j*1
  educalter_10.3 ~ j*1
  educalter_10.4 ~ j*1
  educalter_10.5 ~ j*1
  
  educalter_11.1 ~ j*1
  educalter_11.2 ~ j*1
  educalter_11.3 ~ j*1
  educalter_11.4 ~ j*1
  educalter_11.5 ~ j*1
  
  
  
'



fit <- lavaan(myModel, data = datalw, missing = 'ML', meanstructure = T, int.ov.free = T)
summary(fit, standardized = T)

#> lavaan 0.6-7 ended normally after 93 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of free parameters                         90
#>   Number of equality constraints                    56
#>                                                       
#>   Number of observations                          2575
#>   Number of missing patterns                      1612
#>                                                       
#> Model Test User Model:
#>                                                       
#>   Test statistic                              4684.862
#>   Degrees of freedom                               461
#>   P-value (Chi-square)                           0.000
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Observed
#>   Observed information based on                Hessian
#> 
#> Latent Variables:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   Feducalter_7 =~                                                       
#>     educalter_7.1     1.000                               1.628    0.580
#>     educalter_7.2     1.000                               1.628    0.580
#>     educalter_7.3     1.000                               1.628    0.580
#>     educalter_7.4     1.000                               1.628    0.580
#>     educalter_7.5     1.000                               1.628    0.580
#>   Feducalter_8 =~                                                       
#>     educalter_8.1     1.000                               1.620    0.594
#>     educalter_8.2     1.000                               1.620    0.594
#>     educalter_8.3     1.000                               1.620    0.594
#>     educalter_8.4     1.000                               1.620    0.594
#>     educalter_8.5     1.000                               1.620    0.594
#>   Feducalter_9 =~                                                       
#>     educalter_9.1     1.000                               1.626    0.603
#>     educalter_9.2     1.000                               1.626    0.603
#>     educalter_9.3     1.000                               1.626    0.603
#>     educalter_9.4     1.000                               1.626    0.603
#>     educalter_9.5     1.000                               1.626    0.603
#>   Feducalter_10 =~                                                      
#>     educalter_10.1    1.000                               1.690    0.613
#>     educalter_10.2    1.000                               1.690    0.613
#>     educalter_10.3    1.000                               1.690    0.613
#>     educalter_10.4    1.000                               1.690    0.613
#>     educalter_10.5    1.000                               1.690    0.613
#>   Feducalter_11 =~                                                      
#>     educalter_11.1    1.000                               1.579    0.573
#>     educalter_11.2    1.000                               1.579    0.573
#>     educalter_11.3    1.000                               1.579    0.573
#>     educalter_11.4    1.000                               1.579    0.573
#>     educalter_11.5    1.000                               1.579    0.573
#> 
#> Regressions:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   eu_8 ~                                                                
#>     eu_7       (a)    0.677    0.008   88.754    0.000    0.677    0.664
#>     Feducltr_7 (b)    0.072    0.007   10.963    0.000    0.118    0.100
#>   eu_9 ~                                                                
#>     eu_8       (a)    0.677    0.008   88.754    0.000    0.677    0.678
#>     Feducltr_8 (b)    0.072    0.007   10.963    0.000    0.117    0.100
#>   eu_10 ~                                                               
#>     eu_9       (a)    0.677    0.008   88.754    0.000    0.677    0.668
#>     Feducltr_9 (b)    0.072    0.007   10.963    0.000    0.118    0.099
#>   eu_11 ~                                                               
#>     eu_10      (a)    0.677    0.008   88.754    0.000    0.677    0.672
#>     Fedcltr_10 (b)    0.072    0.007   10.963    0.000    0.122    0.102
#>   Feducalter_8 ~                                                        
#>     eu_7       (c)    0.018    0.010    1.848    0.065    0.011    0.013
#>     Feducltr_7 (d)    1.022    0.007  155.294    0.000    1.027    1.027
#>   Feducalter_9 ~                                                        
#>     eu_8       (c)    0.018    0.010    1.848    0.065    0.011    0.013
#>     Feducltr_8 (d)    1.022    0.007  155.294    0.000    1.018    1.018
#>   Feducalter_10 ~                                                       
#>     eu_9       (c)    0.018    0.010    1.848    0.065    0.011    0.012
#>     Feducltr_9 (d)    1.022    0.007  155.294    0.000    0.983    0.983
#>   Feducalter_11 ~                                                       
#>     eu_10      (c)    0.018    0.010    1.848    0.065    0.011    0.014
#>     Fedcltr_10 (d)    1.022    0.007  155.294    0.000    1.093    1.093
#> 
#> Covariances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   Feducalter_7 ~~                                                       
#>     eu_7              0.573    0.046   12.554    0.000    0.352    0.304
#>  .Feducalter_8 ~~                                                       
#>    .eu_8             -0.046    0.024   -1.952    0.051   -0.114   -0.136
#>  .Feducalter_9 ~~                                                       
#>    .eu_9             -0.021    0.021   -1.020    0.308   -0.061   -0.074
#>  .Feducalter_10 ~~                                                      
#>    .eu_10            -0.022    0.021   -1.016    0.310   -0.080   -0.095
#>  .Feducalter_11 ~~                                                      
#>    .eu_11            -0.035    0.024   -1.463    0.143   -0.049   -0.058
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>    .Feducltr_8        0.076    0.040    1.917    0.055    0.047    0.047
#>    .Feducltr_9        0.024    0.040    0.590    0.555    0.014    0.014
#>    .Fedcltr_10        0.052    0.041    1.280    0.201    0.031    0.031
#>    .Fedcltr_11       -0.042    0.039   -1.095    0.274   -0.027   -0.027
#>     eu_7              1.263    0.023   55.406    0.000    1.263    1.092
#>    .eu_8              0.470    0.019   24.324    0.000    0.470    0.398
#>    .eu_9              0.367    0.019   18.977    0.000    0.367    0.312
#>    .eu_10             0.547    0.020   28.054    0.000    0.547    0.458
#>    .eu_11             0.535    0.020   26.733    0.000    0.535    0.445
#>    .edcltr_7.1 (j)   12.074    0.043  281.887    0.000   12.074    4.303
#>    .edcltr_7.2 (j)   12.074    0.043  281.887    0.000   12.074    4.303
#>    .edcltr_7.3 (j)   12.074    0.043  281.887    0.000   12.074    4.303
#>    .edcltr_7.4 (j)   12.074    0.043  281.887    0.000   12.074    4.303
#>    .edcltr_7.5 (j)   12.074    0.043  281.887    0.000   12.074    4.303
#>    .edcltr_8.1 (j)   12.074    0.043  281.887    0.000   12.074    4.424
#>    .edcltr_8.2 (j)   12.074    0.043  281.887    0.000   12.074    4.424
#>    .edcltr_8.3 (j)   12.074    0.043  281.887    0.000   12.074    4.424
#>    .edcltr_8.4 (j)   12.074    0.043  281.887    0.000   12.074    4.424
#>    .edcltr_8.5 (j)   12.074    0.043  281.887    0.000   12.074    4.424
#>    .edcltr_9.1 (j)   12.074    0.043  281.887    0.000   12.074    4.481
#>    .edcltr_9.2 (j)   12.074    0.043  281.887    0.000   12.074    4.481
#>    .edcltr_9.3 (j)   12.074    0.043  281.887    0.000   12.074    4.481
#>    .edcltr_9.4 (j)   12.074    0.043  281.887    0.000   12.074    4.481
#>    .edcltr_9.5 (j)   12.074    0.043  281.887    0.000   12.074    4.481
#>    .edclt_10.1 (j)   12.074    0.043  281.887    0.000   12.074    4.383
#>    .edclt_10.2 (j)   12.074    0.043  281.887    0.000   12.074    4.383
#>    .edclt_10.3 (j)   12.074    0.043  281.887    0.000   12.074    4.383
#>    .edclt_10.4 (j)   12.074    0.043  281.887    0.000   12.074    4.383
#>    .edclt_10.5 (j)   12.074    0.043  281.887    0.000   12.074    4.383
#>    .edclt_11.1 (j)   12.074    0.043  281.887    0.000   12.074    4.377
#>    .edclt_11.2 (j)   12.074    0.043  281.887    0.000   12.074    4.377
#>    .edclt_11.3 (j)   12.074    0.043  281.887    0.000   12.074    4.377
#>    .edclt_11.4 (j)   12.074    0.043  281.887    0.000   12.074    4.377
#>    .edclt_11.5 (j)   12.074    0.043  281.887    0.000   12.074    4.377
#>     Feducltr_7        0.000                               0.000    0.000
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>    .edcltr_7.1 (e)    5.225    0.096   54.622    0.000    5.225    0.664
#>    .edcltr_7.2 (e)    5.225    0.096   54.622    0.000    5.225    0.664
#>    .edcltr_7.3 (e)    5.225    0.096   54.622    0.000    5.225    0.664
#>    .edcltr_7.4 (e)    5.225    0.096   54.622    0.000    5.225    0.664
#>    .edcltr_7.5 (e)    5.225    0.096   54.622    0.000    5.225    0.664
#>    .edcltr_8.1 (f)    4.824    0.087   55.707    0.000    4.824    0.648
#>    .edcltr_8.2 (f)    4.824    0.087   55.707    0.000    4.824    0.648
#>    .edcltr_8.3 (f)    4.824    0.087   55.707    0.000    4.824    0.648
#>    .edcltr_8.4 (f)    4.824    0.087   55.707    0.000    4.824    0.648
#>    .edcltr_8.5 (f)    4.824    0.087   55.707    0.000    4.824    0.648
#>    .edcltr_9.1 (g)    4.617    0.082   56.602    0.000    4.617    0.636
#>    .edcltr_9.2 (g)    4.617    0.082   56.602    0.000    4.617    0.636
#>    .edcltr_9.3 (g)    4.617    0.082   56.602    0.000    4.617    0.636
#>    .edcltr_9.4 (g)    4.617    0.082   56.602    0.000    4.617    0.636
#>    .edcltr_9.5 (g)    4.617    0.082   56.602    0.000    4.617    0.636
#>    .edclt_10.1 (h)    4.732    0.085   55.399    0.000    4.732    0.624
#>    .edclt_10.2 (h)    4.732    0.085   55.399    0.000    4.732    0.624
#>    .edclt_10.3 (h)    4.732    0.085   55.399    0.000    4.732    0.624
#>    .edclt_10.4 (h)    4.732    0.085   55.399    0.000    4.732    0.624
#>    .edclt_10.5 (h)    4.732    0.085   55.399    0.000    4.732    0.624
#>    .edclt_11.1 (i)    5.115    0.104   49.074    0.000    5.115    0.672
#>    .edclt_11.2 (i)    5.115    0.104   49.074    0.000    5.115    0.672
#>    .edclt_11.3 (i)    5.115    0.104   49.074    0.000    5.115    0.672
#>    .edclt_11.4 (i)    5.115    0.104   49.074    0.000    5.115    0.672
#>    .edclt_11.5 (i)    5.115    0.104   49.074    0.000    5.115    0.672
#>     eu_7              1.338    0.037   35.882    0.000    1.338    1.000
#>    .eu_8              0.708    0.020   35.531    0.000    0.708    0.509
#>    .eu_9              0.680    0.019   35.645    0.000    0.680    0.490
#>    .eu_10             0.720    0.020   35.695    0.000    0.720    0.504
#>    .eu_11             0.720    0.020   35.671    0.000    0.720    0.498
#>     Feducltr_7        2.650    0.106   24.976    0.000    1.000    1.000
#>    .Feducltr_8       -0.163    0.049   -3.318    0.001   -0.062   -0.062
#>    .Feducltr_9       -0.119    0.044   -2.695    0.007   -0.045   -0.045
#>    .Fedcltr_10        0.073    0.050    1.459    0.145    0.026    0.026
#>    .Fedcltr_11       -0.509    0.055   -9.208    0.000   -0.204   -0.204

---

five wave CLPM five indicators two step

myModel <- '
  # Estimate the lagged effects (constrained)
  eu_8   ~ a*eu_7 + b*Feducalter_7
  eu_9   ~ a*eu_8 + b*Feducalter_8
  eu_10  ~ a*eu_9 + b*Feducalter_9
  eu_11  ~ a*eu_10 + b*Feducalter_10
  
  Feducalter_8  ~ c*eu_7 + d*Feducalter_7
  Feducalter_9  ~ c*eu_8 + d*Feducalter_8
  Feducalter_10  ~ c*eu_9 + d*Feducalter_9
  Feducalter_11  ~ c*eu_10 + d*Feducalter_10
  
  # Estimate the covariance at the first wave. 
  eu_7 ~~ Feducalter_7 # Covariance

  # Estimate the covariances between the residuals
  eu_8 ~~ Feducalter_8
  eu_9 ~~ Feducalter_9
  eu_10 ~~ Feducalter_10
  eu_11 ~~ Feducalter_11
  
  # Estimate the variance 
  eu_7 ~~ eu_7 
  Feducalter_7 ~~ Feducalter_7
  
  # Estimate the residual variance
  eu_8 ~~ eu_8 
  Feducalter_8 ~~ Feducalter_8
  eu_9 ~~ eu_9 
  Feducalter_9 ~~ Feducalter_9
  eu_10 ~~ eu_10 
  Feducalter_10 ~~ Feducalter_10
  eu_11 ~~ eu_11 
  Feducalter_11 ~~ Feducalter_11
  
  #intercepts
  Feducalter_7 ~ 1
  Feducalter_8 ~ 1
  Feducalter_9 ~ 1
  Feducalter_10 ~ 1
  Feducalter_11 ~ 1
  
  eu_7 ~ 1
  eu_8 ~ 1
  eu_9 ~ 1
  eu_10 ~ 1
  eu_11 ~ 1
'



fit <- lavaan(myModel, data = datalwb, missing = 'ML', meanstructure = T, int.ov.free = T)
summary(fit, standardized = T)

#> lavaan 0.6-7 ended normally after 23 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of free parameters                         41
#>   Number of equality constraints                    12
#>                                                       
#>   Number of observations                          2575
#>   Number of missing patterns                         2
#>                                                       
#> Model Test User Model:
#>                                                       
#>   Test statistic                              2622.975
#>   Degrees of freedom                                36
#>   P-value (Chi-square)                           0.000
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Observed
#>   Observed information based on                Hessian
#> 
#> Regressions:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   eu_8 ~                                                                
#>     eu_7       (a)    0.693    0.007   95.356    0.000    0.693    0.679
#>     Feducltr_7 (b)    0.077    0.009    8.842    0.000    0.077    0.068
#>   eu_9 ~                                                                
#>     eu_8       (a)    0.693    0.007   95.356    0.000    0.693    0.694
#>     Feducltr_8 (b)    0.077    0.009    8.842    0.000    0.077    0.066
#>   eu_10 ~                                                               
#>     eu_9       (a)    0.693    0.007   95.356    0.000    0.693    0.683
#>     Feducltr_9 (b)    0.077    0.009    8.842    0.000    0.077    0.063
#>   eu_11 ~                                                               
#>     eu_10      (a)    0.693    0.007   95.356    0.000    0.693    0.687
#>     Fedcltr_10 (b)    0.077    0.009    8.842    0.000    0.077    0.062
#>   Feducalter_8 ~                                                        
#>     eu_7       (c)    0.073    0.006   11.633    0.000    0.073    0.084
#>     Feducltr_7 (d)    0.632    0.007   85.127    0.000    0.632    0.650
#>   Feducalter_9 ~                                                        
#>     eu_8       (c)    0.073    0.006   11.633    0.000    0.073    0.087
#>     Feducltr_8 (d)    0.632    0.007   85.127    0.000    0.632    0.649
#>   Feducalter_10 ~                                                       
#>     eu_9       (c)    0.073    0.006   11.633    0.000    0.073    0.089
#>     Feducltr_9 (d)    0.632    0.007   85.127    0.000    0.632    0.644
#>   Feducalter_11 ~                                                       
#>     eu_10      (c)    0.073    0.006   11.633    0.000    0.073    0.093
#>     Fedcltr_10 (d)    0.632    0.007   85.127    0.000    0.632    0.652
#> 
#> Covariances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   eu_7 ~~                                                               
#>     Feducalter_7      0.251    0.025   10.258    0.000    0.251    0.209
#>  .eu_8 ~~                                                               
#>    .Feducalter_8      0.029    0.013    2.274    0.023    0.029    0.046
#>  .eu_9 ~~                                                               
#>    .Feducalter_9      0.004    0.012    0.333    0.739    0.004    0.007
#>  .eu_10 ~~                                                              
#>    .Feducalter_10     0.026    0.012    2.081    0.037    0.026    0.042
#>  .eu_11 ~~                                                              
#>    .Feducalter_11     0.032    0.012    2.733    0.006    0.032    0.055
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     Feducalter_7     -0.003    0.021   -0.131    0.896   -0.003   -0.003
#>    .Feducalter_8      0.009    0.017    0.556    0.578    0.009    0.009
#>    .Feducalter_9      0.005    0.017    0.304    0.761    0.005    0.005
#>    .Feducalter_10     0.063    0.016    3.838    0.000    0.063    0.065
#>    .Feducalter_11    -0.054    0.016   -3.333    0.001   -0.054   -0.058
#>     eu_7              1.263    0.023   55.406    0.000    1.263    1.092
#>    .eu_8              0.450    0.019   23.660    0.000    0.450    0.382
#>    .eu_9              0.346    0.019   18.370    0.000    0.346    0.294
#>    .eu_10             0.525    0.019   27.533    0.000    0.525    0.440
#>    .eu_11             0.509    0.020   25.940    0.000    0.509    0.423
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     eu_7              1.338    0.037   35.882    0.000    1.338    1.000
#>     Feducalter_7      1.079    0.031   35.307    0.000    1.079    1.000
#>    .eu_8              0.716    0.020   35.868    0.000    0.716    0.515
#>    .Feducalter_8      0.560    0.016   35.232    0.000    0.560    0.548
#>    .eu_9              0.683    0.019   35.864    0.000    0.683    0.494
#>    .Feducalter_9      0.529    0.015   35.269    0.000    0.529    0.546
#>    .eu_10             0.727    0.020   35.855    0.000    0.727    0.511
#>    .Feducalter_10     0.518    0.015   35.303    0.000    0.518    0.554
#>    .eu_11             0.732    0.020   35.871    0.000    0.732    0.506
#>    .Feducalter_11     0.474    0.013   35.304    0.000    0.474    0.540

---

---

five wave CLPM aggregation method

myModel <- '
  # Estimate the lagged effects (constrained)
  eu_8   ~ a*eu_7 + b*Meducalter_7
  eu_9   ~ a*eu_8 + b*Meducalter_8
  eu_10  ~ a*eu_9 + b*Meducalter_9
  eu_11  ~ a*eu_10 + b*Meducalter_10
  
  Meducalter_8  ~ c*eu_7 + d*Meducalter_7
  Meducalter_9  ~ c*eu_8 + d*Meducalter_8
  Meducalter_10  ~ c*eu_9 + d*Meducalter_9
  Meducalter_11  ~ c*eu_10 + d*Meducalter_10
  
  # Estimate the covariance at the first wave. 
  eu_7 ~~ Meducalter_7 # Covariance

  # Estimate the covariances between the residuals
  eu_8 ~~ Meducalter_8
  eu_9 ~~ Meducalter_9
  eu_10 ~~ Meducalter_10
  eu_11 ~~ Meducalter_11
  
  # Estimate the variance 
  eu_7 ~~ eu_7 
  Meducalter_7 ~~ Meducalter_7
  
  # Estimate the residual variance
  eu_8 ~~ eu_8 
  Meducalter_8 ~~ Meducalter_8
  eu_9 ~~ eu_9 
  Meducalter_9 ~~ Meducalter_9
  eu_10 ~~ eu_10 
  Meducalter_10 ~~ Meducalter_10
  eu_11 ~~ eu_11 
  Meducalter_11 ~~ Meducalter_11
  
  #intercepts
  Meducalter_7 ~ 1
  Meducalter_8 ~ 1
  Meducalter_9 ~ 1
  Meducalter_10 ~ 1
  Meducalter_11 ~ 1
  
  eu_7 ~ 1
  eu_8 ~ 1
  eu_9 ~ 1
  eu_10 ~ 1
  eu_11 ~ 1
'



fit <- lavaan(myModel, data = datalwb, missing = 'ML', meanstructure = T, int.ov.free = T)
summary(fit, standardized = T)

#> lavaan 0.6-7 ended normally after 47 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of free parameters                         41
#>   Number of equality constraints                    12
#>                                                       
#>   Number of observations                          2575
#>   Number of missing patterns                        32
#>                                                       
#> Model Test User Model:
#>                                                       
#>   Test statistic                              2287.451
#>   Degrees of freedom                                36
#>   P-value (Chi-square)                           0.000
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Observed
#>   Observed information based on                Hessian
#> 
#> Regressions:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   eu_8 ~                                                                
#>     eu_7       (a)    0.691    0.007   94.436    0.000    0.691    0.678
#>     Meducltr_7 (b)    0.038    0.004    8.907    0.000    0.038    0.069
#>   eu_9 ~                                                                
#>     eu_8       (a)    0.691    0.007   94.436    0.000    0.691    0.692
#>     Meducltr_8 (b)    0.038    0.004    8.907    0.000    0.038    0.070
#>   eu_10 ~                                                               
#>     eu_9       (a)    0.691    0.007   94.436    0.000    0.691    0.681
#>     Meducltr_9 (b)    0.038    0.004    8.907    0.000    0.038    0.067
#>   eu_11 ~                                                               
#>     eu_10      (a)    0.691    0.007   94.436    0.000    0.691    0.685
#>     Medcltr_10 (b)    0.038    0.004    8.907    0.000    0.038    0.067
#>   Meducalter_8 ~                                                        
#>     eu_7       (c)    0.138    0.013   10.468    0.000    0.138    0.074
#>     Meducltr_7 (d)    0.723    0.008   95.777    0.000    0.723    0.712
#>   Meducalter_9 ~                                                        
#>     eu_8       (c)    0.138    0.013   10.468    0.000    0.138    0.078
#>     Meducltr_8 (d)    0.723    0.008   95.777    0.000    0.723    0.740
#>   Meducalter_10 ~                                                       
#>     eu_9       (c)    0.138    0.013   10.468    0.000    0.138    0.077
#>     Meducltr_9 (d)    0.723    0.008   95.777    0.000    0.723    0.719
#>   Meducalter_11 ~                                                       
#>     eu_10      (c)    0.138    0.013   10.468    0.000    0.138    0.079
#>     Medcltr_10 (d)    0.723    0.008   95.777    0.000    0.723    0.729
#> 
#> Covariances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   eu_7 ~~                                                               
#>     Meducalter_7      0.550    0.052   10.592    0.000    0.550    0.225
#>  .eu_8 ~~                                                               
#>    .Meducalter_8      0.054    0.027    1.962    0.050    0.054    0.044
#>  .eu_9 ~~                                                               
#>    .Meducalter_9      0.033    0.025    1.337    0.181    0.033    0.030
#>  .eu_10 ~~                                                              
#>    .Meducalter_10     0.050    0.026    1.899    0.058    0.050    0.042
#>  .eu_11 ~~                                                              
#>    .Meducalter_11     0.079    0.027    2.862    0.004    0.079    0.067
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     Meducalter_7     12.105    0.044  275.851    0.000   12.105    5.735
#>    .Meducalter_8      3.260    0.095   34.423    0.000    3.260    1.520
#>    .Meducalter_9      3.227    0.095   34.125    0.000    3.227    1.540
#>    .Meducalter_10     3.285    0.095   34.494    0.000    3.285    1.559
#>    .Meducalter_11     3.207    0.096   33.521    0.000    3.207    1.535
#>     eu_7              1.263    0.023   55.406    0.000    1.263    1.092
#>    .eu_8             -0.011    0.053   -0.201    0.841   -0.011   -0.009
#>    .eu_9             -0.110    0.053   -2.059    0.039   -0.110   -0.093
#>    .eu_10             0.073    0.054    1.354    0.176    0.073    0.061
#>    .eu_11             0.061    0.054    1.137    0.255    0.061    0.051
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     eu_7              1.338    0.037   35.882    0.000    1.338    1.000
#>     Meducalter_7      4.455    0.134   33.356    0.000    4.455    1.000
#>    .eu_8              0.714    0.020   35.841    0.000    0.714    0.515
#>    .Meducalter_8      2.134    0.068   31.221    0.000    2.134    0.464
#>    .eu_9              0.684    0.019   35.843    0.000    0.684    0.494
#>    .Meducalter_9      1.846    0.059   31.157    0.000    1.846    0.420
#>    .eu_10             0.726    0.020   35.836    0.000    0.726    0.510
#>    .Meducalter_10     2.001    0.064   31.171    0.000    2.001    0.451
#>    .eu_11             0.730    0.020   35.842    0.000    0.730    0.504
#>    .Meducalter_11     1.895    0.062   30.538    0.000    1.895    0.434

---

RI five indicators, one-step versus two-step MULDER

one-step

Be aware that Mulder is using cfa and thus allows for all covariances between the factors. Why are the residual variances set to zero? we are assuming that the indicators and the ri perfectly predict the factors. no measurement error.??

RICLPM5.ext3 <- '
  
  #####################
  # MEASUREMENT MODEL #
  #####################
  
  # Factor models for x at 5 waves (constrained). 
  FX1 =~ a*x11 + b*x12 + c*x13
  FX2 =~ a*x21 + b*x22 + c*x23
  FX3 =~ a*x31 + b*x32 + c*x33
  FX4 =~ a*x41 + b*x42 + c*x43
  FX5 =~ a*x51 + b*x52 + c*x53
  
  # Factor models for y at 5 waves (constrained).
  FY1 =~ d*y11 + e*y12 + f*y13
  FY2 =~ d*y21 + e*y22 + f*y23
  FY3 =~ d*y31 + e*y32 + f*y33
  FY4 =~ d*y41 + e*y42 + f*y43
  FY5 =~ d*y51 + e*y52 + f*y53
  
  # Constrained intercepts over time (this is necessary for strong factorial 
  # invariance; without these contraints we have week factorial invariance). 
  x11 + x21 + x31 + x41 + x51 ~ g*1
  x12 + x22 + x32 + x42 + x52 ~ h*1
  x13 + x23 + x33 + x43 + x53 ~ i*1
  y11 + y21 + y31 + y41 + y51 ~ j*1
  y12 + y22 + y32 + y42 + y52 ~ k*1
  y13 + y23 + y33 + y43 + y53 ~ l*1
  
  # Free latent means from t = 2 onward (only do this in combination with the 
  # constraints on the intercepts; without these, this would not be specified).
  FX2 + FX3 + FX4 + FX5 + FY2 + FY3 + FY4 + FY5 ~ 1
  
  ################
  # BETWEEN PART #
  ################
  
  # Create between factors (random intercepts). 
  RIX =~ 1*FX1 + 1*FX2 + 1*FX3 + 1*FX4 + 1*FX5
  RIY =~ 1*FY1 + 1*FY2 + 1*FY3 + 1*FY4 + 1*FY5
  # Set the residual variances of all FX and FY variables to 0. 
  FX1 ~~ 0*FX1
  FX2 ~~ 0*FX2
  FX3 ~~ 0*FX3
  FX4 ~~ 0*FX4
  FX5 ~~ 0*FX5
  FY1 ~~ 0*FY1
  FY2 ~~ 0*FY2
  FY3 ~~ 0*FY3
  FY4 ~~ 0*FY4
  FY5 ~~ 0*FY5
  
  ###############
  # WITHIN PART #
  ###############
 
  # Create the within-part.
  WFX1 =~ 1*FX1
  WFX2 =~ 1*FX2
  WFX3 =~ 1*FX3
  WFX4 =~ 1*FX4
  WFX5 =~ 1*FX5
  
  WFY1 =~ 1*FY1
  WFY2 =~ 1*FY2
  WFY3 =~ 1*FY3
  WFY4 =~ 1*FY4
  WFY5 =~ 1*FY5
  
  # Specify the lagged effects between the within-person centered latent variables.
  WFX2 + WFY2 ~ WFX1 + WFY1
  WFX3 + WFY3 ~ WFX2 + WFY2
  WFX4 + WFY4 ~ WFX3 + WFY3
  WFX5 + WFY5 ~ WFX4 + WFY4
  
  # Estimate the correlations within the same wave.
  WFX2 ~~ WFY2
  WFX3 ~~ WFY3 
  WFX4 ~~ WFY4
  WFX5 ~~ WFY5
  
  ##########################
  # ADDITIONAL CONSTRAINTS #
  ##########################
  
  # Set correlations between the between-factors (random intercepts) and within-
  # factors at wave 1 at 0. 
  RIX + RIY ~~ 0*WFX1 + 0*WFY1
'
RICLPM5.ext3.fit <- cfa(RICLPM5.ext3, data = datMI, missing = 'ML') 
summary(RICLPM5.ext3.fit, standardized = T)

#> lavaan 0.6-7 ended normally after 105 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of free parameters                        122
#>   Number of equality constraints                    40
#>                                                       
#>   Number of observations                          1189
#>   Number of missing patterns                         1
#>                                                       
#> Model Test User Model:
#>                                                       
#>   Test statistic                               381.605
#>   Degrees of freedom                               413
#>   P-value (Chi-square)                           0.864
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Observed
#>   Observed information based on                Hessian
#> 
#> Latent Variables:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   FX1 =~                                                                
#>     x11        (a)    1.000                               0.294    0.391
#>     x12        (b)    0.847    0.098    8.663    0.000    0.249    0.318
#>     x13        (c)    0.779    0.091    8.578    0.000    0.229    0.310
#>   FX2 =~                                                                
#>     x21        (a)    1.000                               0.223    0.307
#>     x22        (b)    0.847    0.098    8.663    0.000    0.189    0.254
#>     x23        (c)    0.779    0.091    8.578    0.000    0.174    0.244
#>   FX3 =~                                                                
#>     x31        (a)    1.000                               0.243    0.344
#>     x32        (b)    0.847    0.098    8.663    0.000    0.206    0.288
#>     x33        (c)    0.779    0.091    8.578    0.000    0.189    0.250
#>   FX4 =~                                                                
#>     x41        (a)    1.000                               0.263    0.348
#>     x42        (b)    0.847    0.098    8.663    0.000    0.222    0.298
#>     x43        (c)    0.779    0.091    8.578    0.000    0.205    0.272
#>   FX5 =~                                                                
#>     x51        (a)    1.000                               0.239    0.322
#>     x52        (b)    0.847    0.098    8.663    0.000    0.202    0.270
#>     x53        (c)    0.779    0.091    8.578    0.000    0.186    0.253
#>   FY1 =~                                                                
#>     y11        (d)    1.000                               0.289    0.371
#>     y12        (e)    1.129    0.081   13.866    0.000    0.326    0.416
#>     y13        (f)    1.140    0.080   14.172    0.000    0.329    0.426
#>   FY2 =~                                                                
#>     y21        (d)    1.000                               0.317    0.411
#>     y22        (e)    1.129    0.081   13.866    0.000    0.358    0.479
#>     y23        (f)    1.140    0.080   14.172    0.000    0.361    0.447
#>   FY3 =~                                                                
#>     y31        (d)    1.000                               0.263    0.347
#>     y32        (e)    1.129    0.081   13.866    0.000    0.297    0.377
#>     y33        (f)    1.140    0.080   14.172    0.000    0.300    0.377
#>   FY4 =~                                                                
#>     y41        (d)    1.000                               0.291    0.371
#>     y42        (e)    1.129    0.081   13.866    0.000    0.329    0.425
#>     y43        (f)    1.140    0.080   14.172    0.000    0.332    0.432
#>   FY5 =~                                                                
#>     y51        (d)    1.000                               0.310    0.398
#>     y52        (e)    1.129    0.081   13.866    0.000    0.350    0.442
#>     y53        (f)    1.140    0.080   14.172    0.000    0.354    0.457
#>   RIX =~                                                                
#>     FX1               1.000                               0.410    0.410
#>     FX2               1.000                               0.541    0.541
#>     FX3               1.000                               0.496    0.496
#>     FX4               1.000                               0.459    0.459
#>     FX5               1.000                               0.505    0.505
#>   RIY =~                                                                
#>     FY1               1.000                               0.523    0.523
#>     FY2               1.000                               0.477    0.477
#>     FY3               1.000                               0.575    0.575
#>     FY4               1.000                               0.519    0.519
#>     FY5               1.000                               0.487    0.487
#>   WFX1 =~                                                               
#>     FX1               1.000                               0.912    0.912
#>   WFX2 =~                                                               
#>     FX2               1.000                               0.841    0.841
#>   WFX3 =~                                                               
#>     FX3               1.000                               0.868    0.868
#>   WFX4 =~                                                               
#>     FX4               1.000                               0.888    0.888
#>   WFX5 =~                                                               
#>     FX5               1.000                               0.863    0.863
#>   WFY1 =~                                                               
#>     FY1               1.000                               0.852    0.852
#>   WFY2 =~                                                               
#>     FY2               1.000                               0.879    0.879
#>   WFY3 =~                                                               
#>     FY3               1.000                               0.818    0.818
#>   WFY4 =~                                                               
#>     FY4               1.000                               0.855    0.855
#>   WFY5 =~                                                               
#>     FY5               1.000                               0.873    0.873
#> 
#> Regressions:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   WFX2 ~                                                                
#>     WFX1              0.227    0.142    1.597    0.110    0.324    0.324
#>     WFY1             -0.239    0.145   -1.645    0.100   -0.313   -0.313
#>   WFY2 ~                                                                
#>     WFX1              0.044    0.119    0.368    0.713    0.042    0.042
#>     WFY1              0.214    0.143    1.492    0.136    0.189    0.189
#>   WFX3 ~                                                                
#>     WFX2              0.181    0.257    0.703    0.482    0.161    0.161
#>     WFY2             -0.187    0.113   -1.659    0.097   -0.246   -0.246
#>   WFY3 ~                                                                
#>     WFX2              0.236    0.199    1.184    0.236    0.206    0.206
#>     WFY2              0.404    0.100    4.035    0.000    0.523    0.523
#>   WFX4 ~                                                                
#>     WFX3              0.494    0.210    2.349    0.019    0.447    0.447
#>     WFY3              0.027    0.164    0.164    0.870    0.025    0.025
#>   WFY4 ~                                                                
#>     WFX3             -0.127    0.170   -0.747    0.455   -0.108   -0.108
#>     WFY3              0.643    0.167    3.843    0.000    0.555    0.555
#>   WFX5 ~                                                                
#>     WFX4              0.227    0.176    1.293    0.196    0.257    0.257
#>     WFY4             -0.018    0.125   -0.145    0.885   -0.022   -0.022
#>   WFY5 ~                                                                
#>     WFX4              0.094    0.147    0.643    0.521    0.081    0.081
#>     WFY4              0.439    0.125    3.503    0.000    0.403    0.403
#> 
#> Covariances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>  .WFX2 ~~                                                               
#>    .WFY2             -0.007    0.008   -0.902    0.367   -0.151   -0.151
#>  .WFX3 ~~                                                               
#>    .WFY3              0.002    0.007    0.333    0.739    0.066    0.066
#>  .WFX4 ~~                                                               
#>    .WFY4             -0.001    0.008   -0.171    0.864   -0.031   -0.031
#>  .WFX5 ~~                                                               
#>    .WFY5              0.003    0.007    0.456    0.649    0.068    0.068
#>   RIX ~~                                                                
#>     WFX1              0.000                               0.000    0.000
#>     WFY1              0.000                               0.000    0.000
#>   RIY ~~                                                                
#>     WFX1              0.000                               0.000    0.000
#>     WFY1              0.000                               0.000    0.000
#>   RIX ~~                                                                
#>     RIY               0.016    0.004    3.764    0.000    0.901    0.901
#>   WFX1 ~~                                                               
#>     WFY1             -0.009    0.008   -1.026    0.305   -0.130   -0.130
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>    .x11        (g)    0.272    0.018   15.080    0.000    0.272    0.361
#>    .x21        (g)    0.272    0.018   15.080    0.000    0.272    0.375
#>    .x31        (g)    0.272    0.018   15.080    0.000    0.272    0.385
#>    .x41        (g)    0.272    0.018   15.080    0.000    0.272    0.360
#>    .x51        (g)    0.272    0.018   15.080    0.000    0.272    0.367
#>    .x12        (h)    0.253    0.017   15.133    0.000    0.253    0.324
#>    .x22        (h)    0.253    0.017   15.133    0.000    0.253    0.340
#>    .x32        (h)    0.253    0.017   15.133    0.000    0.253    0.354
#>    .x42        (h)    0.253    0.017   15.133    0.000    0.253    0.339
#>    .x52        (h)    0.253    0.017   15.133    0.000    0.253    0.337
#>    .x13        (i)    0.268    0.016   16.820    0.000    0.268    0.363
#>    .x23        (i)    0.268    0.016   16.820    0.000    0.268    0.376
#>    .x33        (i)    0.268    0.016   16.820    0.000    0.268    0.353
#>    .x43        (i)    0.268    0.016   16.820    0.000    0.268    0.356
#>    .x53        (i)    0.268    0.016   16.820    0.000    0.268    0.365
#>    .y11        (j)    0.324    0.016   20.376    0.000    0.324    0.417
#>    .y21        (j)    0.324    0.016   20.376    0.000    0.324    0.421
#>    .y31        (j)    0.324    0.016   20.376    0.000    0.324    0.429
#>    .y41        (j)    0.324    0.016   20.376    0.000    0.324    0.413
#>    .y51        (j)    0.324    0.016   20.376    0.000    0.324    0.416
#>    .y12        (k)    0.331    0.017   19.214    0.000    0.331    0.422
#>    .y22        (k)    0.331    0.017   19.214    0.000    0.331    0.444
#>    .y32        (k)    0.331    0.017   19.214    0.000    0.331    0.421
#>    .y42        (k)    0.331    0.017   19.214    0.000    0.331    0.428
#>    .y52        (k)    0.331    0.017   19.214    0.000    0.331    0.418
#>    .y13        (l)    0.325    0.017   18.742    0.000    0.325    0.420
#>    .y23        (l)    0.325    0.017   18.742    0.000    0.325    0.401
#>    .y33        (l)    0.325    0.017   18.742    0.000    0.325    0.408
#>    .y43        (l)    0.325    0.017   18.742    0.000    0.325    0.422
#>    .y53        (l)    0.325    0.017   18.742    0.000    0.325    0.419
#>    .FX2              -0.077    0.021   -3.713    0.000   -0.346   -0.346
#>    .FX3              -0.074    0.022   -3.416    0.001   -0.303   -0.303
#>    .FX4              -0.158    0.023   -6.753    0.000   -0.600   -0.600
#>    .FX5              -0.179    0.023   -7.636    0.000   -0.752   -0.752
#>    .FY2               0.034    0.018    1.897    0.058    0.109    0.109
#>    .FY3               0.016    0.018    0.906    0.365    0.063    0.063
#>    .FY4               0.048    0.018    2.593    0.010    0.164    0.164
#>    .FY5               0.052    0.019    2.791    0.005    0.169    0.169
#>    .FX1               0.000                               0.000    0.000
#>    .FY1               0.000                               0.000    0.000
#>     RIX               0.000                               0.000    0.000
#>     RIY               0.000                               0.000    0.000
#>     WFX1              0.000                               0.000    0.000
#>    .WFX2              0.000                               0.000    0.000
#>    .WFX3              0.000                               0.000    0.000
#>    .WFX4              0.000                               0.000    0.000
#>    .WFX5              0.000                               0.000    0.000
#>     WFY1              0.000                               0.000    0.000
#>    .WFY2              0.000                               0.000    0.000
#>    .WFY3              0.000                               0.000    0.000
#>    .WFY4              0.000                               0.000    0.000
#>    .WFY5              0.000                               0.000    0.000
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>    .FX1               0.000                               0.000    0.000
#>    .FX2               0.000                               0.000    0.000
#>    .FX3               0.000                               0.000    0.000
#>    .FX4               0.000                               0.000    0.000
#>    .FX5               0.000                               0.000    0.000
#>    .FY1               0.000                               0.000    0.000
#>    .FY2               0.000                               0.000    0.000
#>    .FY3               0.000                               0.000    0.000
#>    .FY4               0.000                               0.000    0.000
#>    .FY5               0.000                               0.000    0.000
#>    .x11               0.479    0.026   18.584    0.000    0.479    0.847
#>    .x12               0.549    0.026   20.982    0.000    0.549    0.899
#>    .x13               0.493    0.023   21.370    0.000    0.493    0.904
#>    .x21               0.477    0.023   20.329    0.000    0.477    0.905
#>    .x22               0.517    0.023   22.082    0.000    0.517    0.935
#>    .x23               0.478    0.021   22.353    0.000    0.478    0.941
#>    .x31               0.441    0.023   19.256    0.000    0.441    0.882
#>    .x32               0.469    0.022   21.289    0.000    0.469    0.917
#>    .x33               0.539    0.024   22.583    0.000    0.539    0.938
#>    .x41               0.500    0.025   19.841    0.000    0.500    0.879
#>    .x42               0.506    0.024   21.169    0.000    0.506    0.911
#>    .x43               0.526    0.024   21.573    0.000    0.526    0.926
#>    .x51               0.492    0.025   19.637    0.000    0.492    0.896
#>    .x52               0.522    0.024   21.852    0.000    0.522    0.927
#>    .x53               0.505    0.023   21.990    0.000    0.505    0.936
#>    .y11               0.523    0.025   21.185    0.000    0.523    0.862
#>    .y12               0.509    0.025   19.971    0.000    0.509    0.827
#>    .y13               0.488    0.025   19.378    0.000    0.488    0.818
#>    .y21               0.494    0.024   20.929    0.000    0.494    0.831
#>    .y22               0.429    0.023   18.996    0.000    0.429    0.770
#>    .y23               0.523    0.026   20.020    0.000    0.523    0.800
#>    .y31               0.503    0.023   21.725    0.000    0.503    0.879
#>    .y32               0.531    0.025   20.917    0.000    0.531    0.858
#>    .y33               0.542    0.026   21.161    0.000    0.542    0.858
#>    .y41               0.531    0.025   21.501    0.000    0.531    0.862
#>    .y42               0.491    0.024   20.214    0.000    0.491    0.820
#>    .y43               0.480    0.024   20.207    0.000    0.480    0.813
#>    .y51               0.511    0.024   20.929    0.000    0.511    0.841
#>    .y52               0.506    0.025   19.870    0.000    0.506    0.805
#>    .y53               0.474    0.025   19.165    0.000    0.474    0.791
#>     RIX               0.015    0.006    2.371    0.018    1.000    1.000
#>     RIY               0.023    0.007    3.455    0.001    1.000    1.000
#>     WFX1              0.072    0.017    4.102    0.000    1.000    1.000
#>    .WFX2              0.027    0.014    1.988    0.047    0.771    0.771
#>    .WFX3              0.040    0.014    2.864    0.004    0.899    0.899
#>    .WFX4              0.044    0.015    2.891    0.004    0.801    0.801
#>    .WFX5              0.040    0.014    2.811    0.005    0.933    0.933
#>     WFY1              0.061    0.012    4.931    0.000    1.000    1.000
#>    .WFY2              0.075    0.013    5.983    0.000    0.965    0.965
#>    .WFY3              0.033    0.010    3.291    0.001    0.723    0.723
#>    .WFY4              0.042    0.011    3.895    0.000    0.675    0.675
#>    .WFY5              0.061    0.011    5.362    0.000    0.835    0.835

two-step

RICLPM5.ext3 <- '
  
  ################
  # BETWEEN PART #
  ################
  
  # Create between factors (random intercepts). 
  RIX =~ 1*FX1 + 1*FX2 + 1*FX3 + 1*FX4 + 1*FX5
  RIY =~ 1*FY1 + 1*FY2 + 1*FY3 + 1*FY4 + 1*FY5
  
  # Estimate the variance and covariance of the random intercepts. 
  RIX ~~ RIX
  RIY ~~ RIY
  RIX ~~ RIY
  
  
  ###############
  # WITHIN PART #
  ###############
 
  # Create the within-part.
  WFX1 =~ 1*FX1
  WFX2 =~ 1*FX2
  WFX3 =~ 1*FX3
  WFX4 =~ 1*FX4
  WFX5 =~ 1*FX5
  
  WFY1 =~ 1*FY1
  WFY2 =~ 1*FY2
  WFY3 =~ 1*FY3
  WFY4 =~ 1*FY4
  WFY5 =~ 1*FY5
  
  # Specify the lagged effects between the within-person centered latent variables.
  WFX2 + WFY2 ~ WFX1 + WFY1
  WFX3 + WFY3 ~ WFX2 + WFY2
  WFX4 + WFY4 ~ WFX3 + WFY3
  WFX5 + WFY5 ~ WFX4 + WFY4
  
  # Estimate the COVARIANCE within the same wave.
  WFX2 ~~ WFY2
  
  # Estimate the RESIDUAL COVARIANCE within the same wave.
  WFX2 ~~ WFY2
  WFX3 ~~ WFY3 
  WFX4 ~~ WFY4
  WFX5 ~~ WFY5
  
  # Estimate the (residual) variance of the within-person centered variables.
  WFX1 ~~ WFX1 # Variances
  WFY1 ~~ WFY1 # Variances
  WFX2 ~~ WFX2 # Residual variances
  WFX3 ~~ WFX3 # Residual variances
  WFX4 ~~ WFX4 # Residual variances
  WFX5 ~~ WFX5 # Residual variances
  WFY2 ~~ WFY2 # Residual variances
  WFY3 ~~ WFY3 # Residual variances
  WFY4 ~~ WFY4 # Residual variances
  WFY5 ~~ WFY5 # Residual variances
  
  
  # intercepts
  FX1 ~ 1
  FX2 ~ 1
  FX3 ~ 1
  FX4 ~ 1
  FX5 ~ 1
  
  FY1 ~ 1
  FY2 ~ 1
  FY3 ~ 1
  FY4 ~ 1
  FY5 ~ 1
  
  
  ##########################
  # ADDITIONAL CONSTRAINTS #
  ##########################
  
  # Set correlations between the between-factors (random intercepts) and within-
  # factors at wave 1 at 0. 
  RIX + RIY ~~ 0*WFX1 + 0*WFY1
'

RICLPM5.ext3.fit <- lavaan(RICLPM5.ext3, data = datMIb, missing = 'ML', meanstructure = T, int.ov.free = T)
summary(RICLPM5.ext3.fit, standardized = T)

#> lavaan 0.6-7 ended normally after 201 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of free parameters                         43
#>                                                       
#>   Number of observations                          1189
#>   Number of missing patterns                         1
#>                                                       
#> Model Test User Model:
#>                                                       
#>   Test statistic                              1051.841
#>   Degrees of freedom                                22
#>   P-value (Chi-square)                           0.000
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Observed
#>   Observed information based on                Hessian
#> 
#> Latent Variables:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   RIX =~                                                                
#>     FX1               1.000                               0.060    0.314
#>     FX2               1.000                               0.060    0.485
#>     FX3               1.000                               0.060    0.456
#>     FX4               1.000                               0.060    0.416
#>     FX5               1.000                               0.060    0.492
#>   RIY =~                                                                
#>     FY1               1.000                               0.150    0.673
#>     FY2               1.000                               0.150    0.585
#>     FY3               1.000                               0.150    0.763
#>     FY4               1.000                               0.150    0.709
#>     FY5               1.000                               0.150    0.684
#>   WFX1 =~                                                               
#>     FX1               1.000                               0.182    0.949
#>   WFX2 =~                                                               
#>     FX2               1.000                               0.109    0.874
#>   WFX3 =~                                                               
#>     FX3               1.000                               0.118    0.890
#>   WFX4 =~                                                               
#>     FX4               1.000                               0.132    0.909
#>   WFX5 =~                                                               
#>     FX5               1.000                               0.107    0.871
#>   WFY1 =~                                                               
#>     FY1               1.000                               0.164    0.739
#>   WFY2 =~                                                               
#>     FY2               1.000                               0.207    0.811
#>   WFY3 =~                                                               
#>     FY3               1.000                               0.127    0.646
#>   WFY4 =~                                                               
#>     FY4               1.000                               0.149    0.705
#>   WFY5 =~                                                               
#>     FY5               1.000                               0.160    0.729
#> 
#> Regressions:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   WFX2 ~                                                                
#>     WFX1              0.475    0.024   20.135    0.000    0.795    0.795
#>     WFY1             -0.311    0.019  -16.144    0.000   -0.470   -0.470
#>   WFY2 ~                                                                
#>     WFX1              0.096    0.032    2.961    0.003    0.084    0.084
#>     WFY1              0.637    0.044   14.466    0.000    0.505    0.505
#>   WFX3 ~                                                                
#>     WFX2              0.525    0.042   12.612    0.000    0.485    0.485
#>     WFY2             -0.205    0.016  -12.604    0.000   -0.361   -0.361
#>   WFY3 ~                                                                
#>     WFX2             -0.009    0.046   -0.198    0.843   -0.008   -0.008
#>     WFY2              0.483    0.017   28.237    0.000    0.789    0.789
#>   WFX4 ~                                                                
#>     WFX3              0.891    0.030   29.798    0.000    0.796    0.796
#>     WFY3              0.075    0.028    2.634    0.008    0.072    0.072
#>   WFY4 ~                                                                
#>     WFX3             -0.183    0.058   -3.181    0.001   -0.145   -0.145
#>     WFY3              0.776    0.049   15.942    0.000    0.662    0.662
#>   WFX5 ~                                                                
#>     WFX4              0.430    0.034   12.576    0.000    0.530    0.530
#>     WFY4             -0.072    0.025   -2.890    0.004   -0.100   -0.100
#>   WFY5 ~                                                                
#>     WFX4             -0.137    0.035   -3.936    0.000   -0.113   -0.113
#>     WFY4              0.546    0.033   16.351    0.000    0.509    0.509
#> 
#> Covariances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   RIX ~~                                                                
#>     RIY               0.017    0.001   20.337    0.000    1.846    1.846
#>  .WFX2 ~~                                                               
#>    .WFY2             -0.003    0.000   -6.246    0.000   -0.398   -0.398
#>  .WFX3 ~~                                                               
#>    .WFY3             -0.002    0.000   -9.503    0.000   -0.301   -0.301
#>  .WFX4 ~~                                                               
#>    .WFY4              0.000    0.000    1.820    0.069    0.054    0.054
#>  .WFX5 ~~                                                               
#>    .WFY5             -0.000    0.000   -0.428    0.669   -0.014   -0.014
#>   RIX ~~                                                                
#>     WFX1              0.000                               0.000    0.000
#>     WFY1              0.000                               0.000    0.000
#>   RIY ~~                                                                
#>     WFX1              0.000                               0.000    0.000
#>     WFY1              0.000                               0.000    0.000
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>    .FX1              -0.000    0.006   -0.000    1.000   -0.000   -0.000
#>    .FX2              -0.077    0.004  -21.491    0.000   -0.077   -0.623
#>    .FX3              -0.074    0.004  -19.240    0.000   -0.074   -0.558
#>    .FX4              -0.158    0.004  -37.605    0.000   -0.158   -1.091
#>    .FX5              -0.180    0.004  -50.542    0.000   -0.180   -1.466
#>    .FY1              -0.000    0.006   -0.000    1.000   -0.000   -0.000
#>    .FY2               0.034    0.007    4.654    0.000    0.034    0.135
#>    .FY3               0.016    0.006    2.892    0.004    0.016    0.084
#>    .FY4               0.048    0.006    7.859    0.000    0.048    0.228
#>    .FY5               0.053    0.006    8.290    0.000    0.053    0.240
#>     RIX               0.000                               0.000    0.000
#>     RIY               0.000                               0.000    0.000
#>     WFX1              0.000                               0.000    0.000
#>    .WFX2              0.000                               0.000    0.000
#>    .WFX3              0.000                               0.000    0.000
#>    .WFX4              0.000                               0.000    0.000
#>    .WFX5              0.000                               0.000    0.000
#>     WFY1              0.000                               0.000    0.000
#>    .WFY2              0.000                               0.000    0.000
#>    .WFY3              0.000                               0.000    0.000
#>    .WFY4              0.000                               0.000    0.000
#>    .WFY5              0.000                               0.000    0.000
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     RIX               0.004    0.001    4.106    0.000    1.000    1.000
#>     RIY               0.022    0.001   15.702    0.000    1.000    1.000
#>     WFX1              0.033    0.002   16.589    0.000    1.000    1.000
#>     WFY1              0.027    0.002   14.171    0.000    1.000    1.000
#>    .WFX2              0.002    0.000    7.476    0.000    0.147    0.147
#>    .WFX3              0.007    0.000   22.434    0.000    0.529    0.529
#>    .WFX4              0.007    0.000   24.835    0.000    0.423    0.423
#>    .WFX5              0.008    0.000   20.716    0.000    0.674    0.674
#>    .WFY2              0.032    0.001   23.521    0.000    0.738    0.738
#>    .WFY3              0.006    0.000   20.176    0.000    0.374    0.374
#>    .WFY4              0.010    0.000   21.608    0.000    0.438    0.438
#>    .WFY5              0.018    0.001   22.051    0.000    0.691    0.691
#>    .FX1               0.000                               0.000    0.000
#>    .FX2               0.000                               0.000    0.000
#>    .FX3               0.000                               0.000    0.000
#>    .FX4               0.000                               0.000    0.000
#>    .FX5               0.000                               0.000    0.000
#>    .FY1               0.000                               0.000    0.000
#>    .FY2               0.000                               0.000    0.000
#>    .FY3               0.000                               0.000    0.000
#>    .FY4               0.000                               0.000    0.000
#>    .FY5               0.000                               0.000    0.000

RI five indicators, one-step versus two-step LISS

RI-CLPM five indicators one-step

myModel <- '
  ##################
  #measurement part#
  ##################
  
  #alters are identical thus equal loadings, variances and intercepts at each time point. 
  
  #constrained loadings
  Feducalter_7 =~ 1*educalter_7.1 + 1*educalter_7.2 + 1*educalter_7.3 +  1*educalter_7.4 + 1*educalter_7.5
  Feducalter_8 =~ 1*educalter_8.1 + 1*educalter_8.2 + 1*educalter_8.3 +  1*educalter_8.4 + 1*educalter_8.5
  Feducalter_9 =~ 1*educalter_9.1 + 1*educalter_9.2 + 1*educalter_9.3 +  1*educalter_9.4 + 1*educalter_9.5
  Feducalter_10 =~ 1*educalter_10.1 + 1*educalter_10.2 + 1*educalter_10.3 +  1*educalter_10.4 + 1*educalter_10.5
  Feducalter_11 =~ 1*educalter_11.1 + 1*educalter_11.2 + 1*educalter_11.3 +  1*educalter_11.4 + 1*educalter_11.5

  #constrained variances
  educalter_7.1 ~~ e*educalter_7.1
  educalter_7.2 ~~ e*educalter_7.2
  educalter_7.3 ~~ e*educalter_7.3
  educalter_7.4 ~~ e*educalter_7.4
  educalter_7.5 ~~ e*educalter_7.5
  
  educalter_8.1 ~~ f*educalter_8.1
  educalter_8.2 ~~ f*educalter_8.2
  educalter_8.3 ~~ f*educalter_8.3
  educalter_8.4 ~~ f*educalter_8.4
  educalter_8.5 ~~ f*educalter_8.5
  
  educalter_9.1 ~~ g*educalter_9.1
  educalter_9.2 ~~ g*educalter_9.2
  educalter_9.3 ~~ g*educalter_9.3
  educalter_9.4 ~~ g*educalter_9.4
  educalter_9.5 ~~ g*educalter_9.5
  
  educalter_10.1 ~~ h*educalter_10.1
  educalter_10.2 ~~ h*educalter_10.2
  educalter_10.3 ~~ h*educalter_10.3
  educalter_10.4 ~~ h*educalter_10.4
  educalter_10.5 ~~ h*educalter_10.5
  
  educalter_11.1 ~~ i*educalter_11.1
  educalter_11.2 ~~ i*educalter_11.2
  educalter_11.3 ~~ i*educalter_11.3
  educalter_11.4 ~~ i*educalter_11.4
  educalter_11.5 ~~ i*educalter_11.5
  
  #constrained intercepts
  educalter_7.1 ~ j*1
  educalter_7.2 ~ j*1
  educalter_7.3 ~ j*1
  educalter_7.4 ~ j*1
  educalter_7.5 ~ j*1
  
  educalter_8.1 ~ j*1
  educalter_8.2 ~ j*1
  educalter_8.3 ~ j*1
  educalter_8.4 ~ j*1
  educalter_8.5 ~ j*1
  
  educalter_9.1 ~ j*1
  educalter_9.2 ~ j*1
  educalter_9.3 ~ j*1
  educalter_9.4 ~ j*1
  educalter_9.5 ~ j*1
  
  educalter_10.1 ~ j*1
  educalter_10.2 ~ j*1
  educalter_10.3 ~ j*1
  educalter_10.4 ~ j*1
  educalter_10.5 ~ j*1
  
  educalter_11.1 ~ j*1
  educalter_11.2 ~ j*1
  educalter_11.3 ~ j*1
  educalter_11.4 ~ j*1
  educalter_11.5 ~ j*1
  
  # Free latent means from t = 2 onward. 
  Feducalter_8 ~ 1
  Feducalter_9 ~ 1
  Feducalter_10 ~ 1
  Feducalter_11 ~ 1

  #################
  #structural part#
  #################
  
  
  # Create between components (random intercepts)
  RIx =~ 1*Feducalter_7 + 1*Feducalter_8 + 1*Feducalter_9 + 1*Feducalter_10 + 1*Feducalter_11
  RIy =~ 1*eu_7 + 1*eu_8 + 1*eu_9 + 1*eu_10 + 1*eu_11

  # Set the residual variances of all FX variables to 0. I DONT UNDERSTAND THIS! no measurement error?? how do we deal with this in the two-step approach? if i do i get negative variance of within components. 
  #Feducalter_7 ~~ 0*Feducalter_7
  #Feducalter_8 ~~ 0*Feducalter_8
  #Feducalter_9 ~~ 0*Feducalter_9
  #Feducalter_10 ~~ 0*Feducalter_10
  #Feducalter_11 ~~ 0*Feducalter_11

  # Create within-person centered variables. 
  wFeducalter_7 =~ 1*Feducalter_7
  wFeducalter_8 =~ 1*Feducalter_8
  wFeducalter_9 =~ 1*Feducalter_9
  wFeducalter_10 =~ 1*Feducalter_10
  wFeducalter_11 =~ 1*Feducalter_11
  weu_7 =~ 1*eu_7
  weu_8 =~ 1*eu_8
  weu_9 =~ 1*eu_9
  weu_10 =~ 1*eu_10
  weu_11 =~ 1*eu_11 
  
  # Estimate the lagged effects (constrained)
  weu_8   ~ a*weu_7 + b*wFeducalter_7
  weu_9   ~ a*weu_8 + b*wFeducalter_8
  weu_10  ~ a*weu_9 + b*wFeducalter_9
  weu_11  ~ a*weu_10 + b*wFeducalter_10
  
  wFeducalter_8  ~ c*weu_7 + d*wFeducalter_7
  wFeducalter_9  ~ c*weu_8 + d*wFeducalter_8
  wFeducalter_10  ~ c*weu_9 + d*wFeducalter_9
  wFeducalter_11  ~ c*weu_10 + d*wFeducalter_10
  
  # Estimate the covariance at the first wave. 
  weu_7 ~~ wFeducalter_7 # Covariance

  # Estimate the covariances between the residuals
  weu_8 ~~ wFeducalter_8
  weu_9 ~~ wFeducalter_9
  weu_10 ~~ wFeducalter_10
  weu_11 ~~ wFeducalter_11
  
  # Estimate the variance 
  weu_7 ~~ weu_7 
  wFeducalter_7 ~~ wFeducalter_7
  
  # Estimate the residual variance
  weu_8 ~~ weu_8 
  wFeducalter_8 ~~ wFeducalter_8
  weu_9 ~~ weu_9 
  wFeducalter_9 ~~ wFeducalter_9
  weu_10 ~~ weu_10 
  wFeducalter_10 ~~ wFeducalter_10
  weu_11 ~~ weu_11 
  wFeducalter_11 ~~ wFeducalter_11
  
  # Estimate the variance and covariance of the random intercepts. 
  RIx ~~ RIx
  RIy ~~ RIy
  RIx ~~ RIy
  
  eu_7 ~ 1
  eu_8 ~ 1
  eu_9 ~ 1
  eu_10 ~ 1
  eu_11 ~ 1
  
  ##########################
  # ADDITIONAL CONSTRAINTS #
  ##########################
  
  # Set correlations between the between-factors (random intercepts) and within-
  # factors at wave 1 at 0. I DONT UNDERSTAND WHY, OR BETTER WHY THIS IS NOT INCLUDED IN THE MODEL WITH ONLY ONE INDICATOR
  
  RIx + RIy ~~ 0*wFeducalter_7 + 0*weu_7
  
  
'



fit <- lavaan(myModel, data = datalw, missing = 'ML', meanstructure = T, int.ov.free = T)
summary(fit, standardized = T)

#> lavaan 0.6-7 ended normally after 74 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of free parameters                         93
#>   Number of equality constraints                    56
#>                                                       
#>   Number of observations                          2575
#>   Number of missing patterns                      1612
#>                                                       
#> Model Test User Model:
#>                                                       
#>   Test statistic                              3037.585
#>   Degrees of freedom                               458
#>   P-value (Chi-square)                           0.000
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Observed
#>   Observed information based on                Hessian
#> 
#> Latent Variables:
#>                     Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   Feducalter_7 =~                                                        
#>     educalter_7.1      1.000                               1.604    0.573
#>     educalter_7.2      1.000                               1.604    0.573
#>     educalter_7.3      1.000                               1.604    0.573
#>     educalter_7.4      1.000                               1.604    0.573
#>     educalter_7.5      1.000                               1.604    0.573
#>   Feducalter_8 =~                                                        
#>     educalter_8.1      1.000                               1.546    0.563
#>     educalter_8.2      1.000                               1.546    0.563
#>     educalter_8.3      1.000                               1.546    0.563
#>     educalter_8.4      1.000                               1.546    0.563
#>     educalter_8.5      1.000                               1.546    0.563
#>   Feducalter_9 =~                                                        
#>     educalter_9.1      1.000                               1.539    0.569
#>     educalter_9.2      1.000                               1.539    0.569
#>     educalter_9.3      1.000                               1.539    0.569
#>     educalter_9.4      1.000                               1.539    0.569
#>     educalter_9.5      1.000                               1.539    0.569
#>   Feducalter_10 =~                                                       
#>     educalter_10.1     1.000                               1.517    0.554
#>     educalter_10.2     1.000                               1.517    0.554
#>     educalter_10.3     1.000                               1.517    0.554
#>     educalter_10.4     1.000                               1.517    0.554
#>     educalter_10.5     1.000                               1.517    0.554
#>   Feducalter_11 =~                                                       
#>     educalter_11.1     1.000                               1.553    0.566
#>     educalter_11.2     1.000                               1.553    0.566
#>     educalter_11.3     1.000                               1.553    0.566
#>     educalter_11.4     1.000                               1.553    0.566
#>     educalter_11.5     1.000                               1.553    0.566
#>   RIx =~                                                                 
#>     Feducalter_7       1.000                               1.048    1.048
#>     Feducalter_8       1.000                               1.088    1.088
#>     Feducalter_9       1.000                               1.092    1.092
#>     Feducalter_10      1.000                               1.108    1.108
#>     Feducalter_11      1.000                               1.083    1.083
#>   RIy =~                                                                 
#>     eu_7               1.000                               0.953    0.814
#>     eu_8               1.000                               0.953    0.808
#>     eu_9               1.000                               0.953    0.811
#>     eu_10              1.000                               0.953    0.805
#>     eu_11              1.000                               0.953    0.800
#>   wFeducalter_7 =~                                                       
#>     Feducalter_7       1.000                                  NA       NA
#>   wFeducalter_8 =~                                                       
#>     Feducalter_8       1.000                                  NA       NA
#>   wFeducalter_9 =~                                                       
#>     Feducalter_9       1.000                                  NA       NA
#>   wFeducalter_10 =~                                                      
#>     Feducalter_10      1.000                                  NA       NA
#>   wFeducalter_11 =~                                                      
#>     Feducalter_11      1.000                                  NA       NA
#>   weu_7 =~                                                               
#>     eu_7               1.000                               0.681    0.581
#>   weu_8 =~                                                               
#>     eu_8               1.000                               0.695    0.589
#>   weu_9 =~                                                               
#>     eu_9               1.000                               0.689    0.586
#>   weu_10 =~                                                              
#>     eu_10              1.000                               0.704    0.594
#>   weu_11 =~                                                              
#>     eu_11              1.000                               0.715    0.600
#> 
#> Regressions:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   weu_8 ~                                                               
#>     weu_7      (a)    0.137    0.015    8.896    0.000    0.134    0.134
#>     wFedcltr_7 (b)   -0.013    0.021   -0.642    0.521       NA       NA
#>   weu_9 ~                                                               
#>     weu_8      (a)    0.137    0.015    8.896    0.000    0.138    0.138
#>     wFedcltr_8 (b)   -0.013    0.021   -0.642    0.521       NA       NA
#>   weu_10 ~                                                              
#>     weu_9      (a)    0.137    0.015    8.896    0.000    0.134    0.134
#>     wFedcltr_9 (b)   -0.013    0.021   -0.642    0.521       NA       NA
#>   weu_11 ~                                                              
#>     weu_10     (a)    0.137    0.015    8.896    0.000    0.134    0.134
#>     wFdcltr_10 (b)   -0.013    0.021   -0.642    0.521       NA       NA
#>   wFeducalter_8 ~                                                       
#>     weu_7      (c)    0.033    0.021    1.544    0.123       NA       NA
#>     wFedcltr_7 (d)   -0.170    0.029   -5.791    0.000       NA       NA
#>   wFeducalter_9 ~                                                       
#>     weu_8      (c)    0.033    0.021    1.544    0.123       NA       NA
#>     wFedcltr_8 (d)   -0.170    0.029   -5.791    0.000       NA       NA
#>   wFeducalter_10 ~                                                      
#>     weu_9      (c)    0.033    0.021    1.544    0.123       NA       NA
#>     wFedcltr_9 (d)   -0.170    0.029   -5.791    0.000       NA       NA
#>   wFeducalter_11 ~                                                      
#>     weu_10     (c)    0.033    0.021    1.544    0.123       NA       NA
#>     wFdcltr_10 (d)   -0.170    0.029   -5.791    0.000       NA       NA
#> 
#> Covariances:
#>                     Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   wFeducalter_7 ~~                                                       
#>     weu_7             -0.008    0.021   -0.373    0.709   -0.022   -0.022
#>  .wFeducalter_8 ~~                                                       
#>    .weu_8              0.018    0.019    0.958    0.338    0.040    0.040
#>  .wFeducalter_9 ~~                                                       
#>    .weu_9              0.013    0.019    0.694    0.488    0.028    0.028
#>  .wFeducalter_10 ~~                                                      
#>    .weu_10             0.014    0.018    0.745    0.456    0.027    0.027
#>  .wFeducalter_11 ~~                                                      
#>    .weu_11             0.008    0.021    0.403    0.687    0.019    0.019
#>   RIx ~~                                                                 
#>     RIy                0.556    0.038   14.482    0.000    0.347    0.347
#>     wFeducalter_7      0.000                               0.000    0.000
#>     weu_7              0.000                               0.000    0.000
#>   RIy ~~                                                                 
#>     wFeducalter_7      0.000                               0.000    0.000
#>     weu_7              0.000                               0.000    0.000
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>    .edcltr_7.1 (j)   12.077    0.042  284.997    0.000   12.077    4.311
#>    .edcltr_7.2 (j)   12.077    0.042  284.997    0.000   12.077    4.311
#>    .edcltr_7.3 (j)   12.077    0.042  284.997    0.000   12.077    4.311
#>    .edcltr_7.4 (j)   12.077    0.042  284.997    0.000   12.077    4.311
#>    .edcltr_7.5 (j)   12.077    0.042  284.997    0.000   12.077    4.311
#>    .edcltr_8.1 (j)   12.077    0.042  284.997    0.000   12.077    4.401
#>    .edcltr_8.2 (j)   12.077    0.042  284.997    0.000   12.077    4.401
#>    .edcltr_8.3 (j)   12.077    0.042  284.997    0.000   12.077    4.401
#>    .edcltr_8.4 (j)   12.077    0.042  284.997    0.000   12.077    4.401
#>    .edcltr_8.5 (j)   12.077    0.042  284.997    0.000   12.077    4.401
#>    .edcltr_9.1 (j)   12.077    0.042  284.997    0.000   12.077    4.464
#>    .edcltr_9.2 (j)   12.077    0.042  284.997    0.000   12.077    4.464
#>    .edcltr_9.3 (j)   12.077    0.042  284.997    0.000   12.077    4.464
#>    .edcltr_9.4 (j)   12.077    0.042  284.997    0.000   12.077    4.464
#>    .edcltr_9.5 (j)   12.077    0.042  284.997    0.000   12.077    4.464
#>    .edclt_10.1 (j)   12.077    0.042  284.997    0.000   12.077    4.415
#>    .edclt_10.2 (j)   12.077    0.042  284.997    0.000   12.077    4.415
#>    .edclt_10.3 (j)   12.077    0.042  284.997    0.000   12.077    4.415
#>    .edclt_10.4 (j)   12.077    0.042  284.997    0.000   12.077    4.415
#>    .edclt_10.5 (j)   12.077    0.042  284.997    0.000   12.077    4.415
#>    .edclt_11.1 (j)   12.077    0.042  284.997    0.000   12.077    4.403
#>    .edclt_11.2 (j)   12.077    0.042  284.997    0.000   12.077    4.403
#>    .edclt_11.3 (j)   12.077    0.042  284.997    0.000   12.077    4.403
#>    .edclt_11.4 (j)   12.077    0.042  284.997    0.000   12.077    4.403
#>    .edclt_11.5 (j)   12.077    0.042  284.997    0.000   12.077    4.403
#>    .Feducltr_8        0.093    0.033    2.789    0.005    0.060    0.060
#>    .Feducltr_9        0.133    0.033    4.011    0.000    0.087    0.087
#>    .Fedcltr_10        0.223    0.033    6.725    0.000    0.147    0.147
#>    .Fedcltr_11        0.224    0.035    6.451    0.000    0.144    0.144
#>    .eu_7              1.263    0.023   54.705    0.000    1.263    1.078
#>    .eu_8              1.325    0.023   56.999    0.000    1.325    1.123
#>    .eu_9              1.272    0.023   54.873    0.000    1.272    1.081
#>    .eu_10             1.419    0.023   60.778    0.000    1.419    1.198
#>    .eu_11             1.512    0.023   64.390    0.000    1.512    1.269
#>    .Feducltr_7        0.000                               0.000    0.000
#>     RIx               0.000                               0.000    0.000
#>     RIy               0.000                               0.000    0.000
#>     wFedcltr_7        0.000                                  NA       NA
#>    .wFedcltr_8        0.000                                  NA       NA
#>    .wFedcltr_9        0.000                                  NA       NA
#>    .wFdcltr_10        0.000                                  NA       NA
#>    .wFdcltr_11        0.000                                  NA       NA
#>     weu_7             0.000                               0.000    0.000
#>    .weu_8             0.000                               0.000    0.000
#>    .weu_9             0.000                               0.000    0.000
#>    .weu_10            0.000                               0.000    0.000
#>    .weu_11            0.000                               0.000    0.000
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>    .edcltr_7.1 (e)    5.274    0.101   52.432    0.000    5.274    0.672
#>    .edcltr_7.2 (e)    5.274    0.101   52.432    0.000    5.274    0.672
#>    .edcltr_7.3 (e)    5.274    0.101   52.432    0.000    5.274    0.672
#>    .edcltr_7.4 (e)    5.274    0.101   52.432    0.000    5.274    0.672
#>    .edcltr_7.5 (e)    5.274    0.101   52.432    0.000    5.274    0.672
#>    .edcltr_8.1 (f)    5.142    0.100   51.327    0.000    5.142    0.683
#>    .edcltr_8.2 (f)    5.142    0.100   51.327    0.000    5.142    0.683
#>    .edcltr_8.3 (f)    5.142    0.100   51.327    0.000    5.142    0.683
#>    .edcltr_8.4 (f)    5.142    0.100   51.327    0.000    5.142    0.683
#>    .edcltr_8.5 (f)    5.142    0.100   51.327    0.000    5.142    0.683
#>    .edcltr_9.1 (g)    4.951    0.095   52.277    0.000    4.951    0.676
#>    .edcltr_9.2 (g)    4.951    0.095   52.277    0.000    4.951    0.676
#>    .edcltr_9.3 (g)    4.951    0.095   52.277    0.000    4.951    0.676
#>    .edcltr_9.4 (g)    4.951    0.095   52.277    0.000    4.951    0.676
#>    .edcltr_9.5 (g)    4.951    0.095   52.277    0.000    4.951    0.676
#>    .edclt_10.1 (h)    5.182    0.102   51.011    0.000    5.182    0.693
#>    .edclt_10.2 (h)    5.182    0.102   51.011    0.000    5.182    0.693
#>    .edclt_10.3 (h)    5.182    0.102   51.011    0.000    5.182    0.693
#>    .edclt_10.4 (h)    5.182    0.102   51.011    0.000    5.182    0.693
#>    .edclt_10.5 (h)    5.182    0.102   51.011    0.000    5.182    0.693
#>    .edclt_11.1 (i)    5.112    0.104   49.156    0.000    5.112    0.679
#>    .edclt_11.2 (i)    5.112    0.104   49.156    0.000    5.112    0.679
#>    .edclt_11.3 (i)    5.112    0.104   49.156    0.000    5.112    0.679
#>    .edclt_11.4 (i)    5.112    0.104   49.156    0.000    5.112    0.679
#>    .edclt_11.5 (i)    5.112    0.104   49.156    0.000    5.112    0.679
#>     weu_7             0.464    0.017   27.587    0.000    1.000    1.000
#>     wFedcltr_7       -0.255    0.045   -5.705    0.000       NA       NA
#>    .weu_8             0.474    0.017   28.261    0.000    0.982    0.982
#>    .wFedcltr_8       -0.431    0.039  -11.072    0.000       NA       NA
#>    .weu_9             0.466    0.016   28.645    0.000    0.981    0.981
#>    .wFedcltr_9       -0.446    0.039  -11.482    0.000       NA       NA
#>    .weu_10            0.486    0.017   28.680    0.000    0.982    0.982
#>    .wFdcltr_10       -0.513    0.037  -13.799    0.000       NA       NA
#>    .weu_11            0.502    0.017   30.160    0.000    0.982    0.982
#>    .wFdcltr_11       -0.400    0.044   -9.048    0.000       NA       NA
#>     RIx               2.827    0.092   30.645    0.000    1.000    1.000
#>     RIy               0.909    0.029   31.329    0.000    1.000    1.000
#>    .eu_7              0.000                               0.000    0.000
#>    .eu_8              0.000                               0.000    0.000
#>    .eu_9              0.000                               0.000    0.000
#>    .eu_10             0.000                               0.000    0.000
#>    .eu_11             0.000                               0.000    0.000
#>    .Feducltr_7        0.000                               0.000    0.000
#>    .Feducltr_8        0.000                               0.000    0.000
#>    .Feducltr_9        0.000                               0.000    0.000
#>    .Fedcltr_10        0.000                               0.000    0.000
#>    .Fedcltr_11        0.000                               0.000    0.000

---

two step

myModel <- '

  ################
  # BETWEEN PART #
  ###############

  # Create between components (random intercepts)
  RIx =~ 1*Feducalter_7 + 1*Feducalter_8 + 1*Feducalter_9 + 1*Feducalter_10 + 1*Feducalter_11
  RIy =~ 1*eu_7 + 1*eu_8 + 1*eu_9 + 1*eu_10 + 1*eu_11

  # Estimate the variance and covariance of the random intercepts. 
  RIx ~~ RIx
  RIy ~~ RIy
  RIx ~~ RIy

  # Set the residual variances of all FX variables to 0. I DONT UNDERSTAND THIS! no measurement error?? 
  Feducalter_7 ~~ 0*Feducalter_7
  Feducalter_8 ~~ 0*Feducalter_8
  Feducalter_9 ~~ 0*Feducalter_9
  Feducalter_10 ~~ 0*Feducalter_10
  Feducalter_11 ~~ 0*Feducalter_11

  ###############
  # WITHIN PART #
  ###############

   # Create within-person centered variables. 
  wFeducalter_7 =~ 1*Feducalter_7
  wFeducalter_8 =~ 1*Feducalter_8
  wFeducalter_9 =~ 1*Feducalter_9
  wFeducalter_10 =~ 1*Feducalter_10
  wFeducalter_11 =~ 1*Feducalter_11
  weu_7 =~ 1*eu_7
  weu_8 =~ 1*eu_8
  weu_9 =~ 1*eu_9
  weu_10 =~ 1*eu_10
  weu_11 =~ 1*eu_11 
  
  # Estimate the lagged effects (constrained)
  weu_8   ~ a*weu_7 + b*wFeducalter_7
  weu_9   ~ a*weu_8 + b*wFeducalter_8
  weu_10  ~ a*weu_9 + b*wFeducalter_9
  weu_11  ~ a*weu_10 + b*wFeducalter_10
  
  wFeducalter_8  ~ c*weu_7 + d*wFeducalter_7
  wFeducalter_9  ~ c*weu_8 + d*wFeducalter_8
  wFeducalter_10  ~ c*weu_9 + d*wFeducalter_9
  wFeducalter_11  ~ c*weu_10 + d*wFeducalter_10
  
  # Estimate the covariance at the first wave. 
  weu_7 ~~ wFeducalter_7 # Covariance

  # Estimate the covariances between the residuals
  weu_8 ~~ wFeducalter_8
  weu_9 ~~ wFeducalter_9
  weu_10 ~~ wFeducalter_10
  weu_11 ~~ wFeducalter_11
  
  # Estimate the variance 
  weu_7 ~~ weu_7 
  wFeducalter_7 ~~ wFeducalter_7
  
  # Estimate the residual variance
  weu_8 ~~ weu_8 
  wFeducalter_8 ~~ wFeducalter_8
  weu_9 ~~ weu_9 
  wFeducalter_9 ~~ wFeducalter_9
  weu_10 ~~ weu_10 
  wFeducalter_10 ~~ wFeducalter_10
  weu_11 ~~ weu_11 
  wFeducalter_11 ~~ wFeducalter_11
  

  
  #intercepts
  Feducalter_7 ~ 1
  Feducalter_8 ~ 1
  Feducalter_9 ~ 1
  Feducalter_10 ~ 1
  Feducalter_11 ~ 1
  
  eu_7 ~ 1
  eu_8 ~ 1
  eu_9 ~ 1
  eu_10 ~ 1
  eu_11 ~ 1
  
  ##########################
  # ADDITIONAL CONSTRAINTS #
  ##########################
  
  # Set correlations between the between-factors (random intercepts) and within-
  # factors at wave 1 at 0. 
  RIx + RIy ~~ 0*wFeducalter_7 + 0*weu_7
  
  
'



fit <- lavaan(myModel, data = datalwb, missing = 'ML', meanstructure = T, int.ov.free = T)
summary(fit, standardized = T)

#> lavaan 0.6-7 ended normally after 34 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of free parameters                         44
#>   Number of equality constraints                    12
#>                                                       
#>   Number of observations                          2575
#>   Number of missing patterns                         2
#>                                                       
#> Model Test User Model:
#>                                                       
#>   Test statistic                                91.502
#>   Degrees of freedom                                33
#>   P-value (Chi-square)                           0.000
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Observed
#>   Observed information based on                Hessian
#> 
#> Latent Variables:
#>                     Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   RIx =~                                                                 
#>     Feducalter_7       1.000                               0.783    0.758
#>     Feducalter_8       1.000                               0.783    0.799
#>     Feducalter_9       1.000                               0.783    0.805
#>     Feducalter_10      1.000                               0.783    0.804
#>     Feducalter_11      1.000                               0.783    0.806
#>   RIy =~                                                                 
#>     eu_7               1.000                               0.954    0.814
#>     eu_8               1.000                               0.954    0.808
#>     eu_9               1.000                               0.954    0.811
#>     eu_10              1.000                               0.954    0.805
#>     eu_11              1.000                               0.954    0.800
#>   wFeducalter_7 =~                                                       
#>     Feducalter_7       1.000                               0.672    0.652
#>   wFeducalter_8 =~                                                       
#>     Feducalter_8       1.000                               0.590    0.602
#>   wFeducalter_9 =~                                                       
#>     Feducalter_9       1.000                               0.577    0.594
#>   wFeducalter_10 =~                                                      
#>     Feducalter_10      1.000                               0.578    0.594
#>   wFeducalter_11 =~                                                      
#>     Feducalter_11      1.000                               0.575    0.592
#>   weu_7 =~                                                               
#>     eu_7               1.000                               0.681    0.581
#>   weu_8 =~                                                               
#>     eu_8               1.000                               0.695    0.589
#>   weu_9 =~                                                               
#>     eu_9               1.000                               0.688    0.585
#>   weu_10 =~                                                              
#>     eu_10              1.000                               0.703    0.594
#>   weu_11 =~                                                              
#>     eu_11              1.000                               0.716    0.600
#> 
#> Regressions:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   weu_8 ~                                                               
#>     weu_7      (a)    0.135    0.015    8.835    0.000    0.133    0.133
#>     wFedcltr_7 (b)    0.024    0.015    1.590    0.112    0.023    0.023
#>   weu_9 ~                                                               
#>     weu_8      (a)    0.135    0.015    8.835    0.000    0.137    0.137
#>     wFedcltr_8 (b)    0.024    0.015    1.590    0.112    0.020    0.020
#>   weu_10 ~                                                              
#>     weu_9      (a)    0.135    0.015    8.835    0.000    0.132    0.132
#>     wFedcltr_9 (b)    0.024    0.015    1.590    0.112    0.019    0.019
#>   weu_11 ~                                                              
#>     weu_10     (a)    0.135    0.015    8.835    0.000    0.133    0.133
#>     wFdcltr_10 (b)    0.024    0.015    1.590    0.112    0.019    0.019
#>   wFeducalter_8 ~                                                       
#>     weu_7      (c)    0.023    0.011    2.082    0.037    0.027    0.027
#>     wFedcltr_7 (d)    0.073    0.014    5.132    0.000    0.083    0.083
#>   wFeducalter_9 ~                                                       
#>     weu_8      (c)    0.023    0.011    2.082    0.037    0.028    0.028
#>     wFedcltr_8 (d)    0.073    0.014    5.132    0.000    0.075    0.075
#>   wFeducalter_10 ~                                                      
#>     weu_9      (c)    0.023    0.011    2.082    0.037    0.027    0.027
#>     wFedcltr_9 (d)    0.073    0.014    5.132    0.000    0.073    0.073
#>   wFeducalter_11 ~                                                      
#>     weu_10     (c)    0.023    0.011    2.082    0.037    0.028    0.028
#>     wFdcltr_10 (d)    0.073    0.014    5.132    0.000    0.073    0.073
#> 
#> Covariances:
#>                     Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   RIx ~~                                                                 
#>     RIy                0.244    0.018   13.736    0.000    0.327    0.327
#>   wFeducalter_7 ~~                                                       
#>     weu_7              0.012    0.011    1.074    0.283    0.027    0.027
#>  .wFeducalter_8 ~~                                                       
#>    .weu_8              0.002    0.010    0.174    0.862    0.004    0.004
#>  .wFeducalter_9 ~~                                                       
#>    .weu_9             -0.000    0.010   -0.035    0.972   -0.001   -0.001
#>  .wFeducalter_10 ~~                                                      
#>    .weu_10             0.009    0.010    0.895    0.371    0.023    0.023
#>  .wFeducalter_11 ~~                                                      
#>    .weu_11             0.012    0.010    1.174    0.240    0.028    0.028
#>   RIx ~~                                                                 
#>     wFeducalter_7      0.000                               0.000    0.000
#>     weu_7              0.000                               0.000    0.000
#>   RIy ~~                                                                 
#>     wFeducalter_7      0.000                               0.000    0.000
#>     weu_7              0.000                               0.000    0.000
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>    .Feducalter_7     -0.003    0.021   -0.127    0.899   -0.003   -0.003
#>    .Feducalter_8      0.100    0.020    5.109    0.000    0.100    0.102
#>    .Feducalter_9      0.165    0.019    8.499    0.000    0.165    0.170
#>    .Feducalter_10     0.260    0.019   13.380    0.000    0.260    0.268
#>    .Feducalter_11     0.214    0.019   11.002    0.000    0.214    0.220
#>    .eu_7              1.263    0.023   54.683    0.000    1.263    1.078
#>    .eu_8              1.325    0.023   56.992    0.000    1.325    1.123
#>    .eu_9              1.272    0.023   54.884    0.000    1.272    1.082
#>    .eu_10             1.419    0.023   60.774    0.000    1.419    1.198
#>    .eu_11             1.512    0.023   64.362    0.000    1.512    1.268
#>     RIx               0.000                               0.000    0.000
#>     RIy               0.000                               0.000    0.000
#>     wFeducalter_7     0.000                               0.000    0.000
#>    .wFeducalter_8     0.000                               0.000    0.000
#>    .wFeducalter_9     0.000                               0.000    0.000
#>    .wFeducalter_10    0.000                               0.000    0.000
#>    .wFeducalter_11    0.000                               0.000    0.000
#>     weu_7             0.000                               0.000    0.000
#>    .weu_8             0.000                               0.000    0.000
#>    .weu_9             0.000                               0.000    0.000
#>    .weu_10            0.000                               0.000    0.000
#>    .weu_11            0.000                               0.000    0.000
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     RIx               0.612    0.020   30.827    0.000    1.000    1.000
#>     RIy               0.909    0.029   31.333    0.000    1.000    1.000
#>    .Feducalter_7      0.000                               0.000    0.000
#>    .Feducalter_8      0.000                               0.000    0.000
#>    .Feducalter_9      0.000                               0.000    0.000
#>    .Feducalter_10     0.000                               0.000    0.000
#>    .Feducalter_11     0.000                               0.000    0.000
#>     weu_7             0.464    0.017   27.564    0.000    1.000    1.000
#>     wFeducalter_7     0.452    0.015   29.552    0.000    1.000    1.000
#>    .weu_8             0.474    0.017   28.238    0.000    0.982    0.982
#>    .wFeducalter_8     0.345    0.012   27.662    0.000    0.992    0.992
#>    .weu_9             0.464    0.016   28.618    0.000    0.981    0.981
#>    .wFeducalter_9     0.331    0.012   27.724    0.000    0.994    0.994
#>    .weu_10            0.486    0.017   28.672    0.000    0.982    0.982
#>    .wFeducalter_10    0.332    0.012   27.593    0.000    0.994    0.994
#>    .weu_11            0.503    0.017   30.154    0.000    0.982    0.982
#>    .wFeducalter_11    0.328    0.011   28.650    0.000    0.994    0.994
#>    .eu_7              0.000                               0.000    0.000
#>    .eu_8              0.000                               0.000    0.000
#>    .eu_9              0.000                               0.000    0.000
#>    .eu_10             0.000                               0.000    0.000
#>    .eu_11             0.000                               0.000    0.000

---

include educational level ego

I do not really understand why the cross-lagged effects become smaller after introduction of educego.

educego not included

myModel <- '

  # Create between components (random intercepts)
  RIx =~ 1*Feducalter_7 + 1*Feducalter_8 + 1*Feducalter_9 + 1*Feducalter_10 + 1*Feducalter_11
  RIy =~ 1*eu_7 + 1*eu_8 + 1*eu_9 + 1*eu_10 + 1*eu_11

   # Create within-person centered variables. 
  wFeducalter_7 =~ 1*Feducalter_7
  wFeducalter_8 =~ 1*Feducalter_8
  wFeducalter_9 =~ 1*Feducalter_9
  wFeducalter_10 =~ 1*Feducalter_10
  wFeducalter_11 =~ 1*Feducalter_11
  weu_7 =~ 1*eu_7
  weu_8 =~ 1*eu_8
  weu_9 =~ 1*eu_9
  weu_10 =~ 1*eu_10
  weu_11 =~ 1*eu_11 
  
  # Estimate the lagged effects (constrained)
  weu_8   ~ a*weu_7 + b*wFeducalter_7
  weu_9   ~ a*weu_8 + b*wFeducalter_8
  weu_10  ~ a*weu_9 + b*wFeducalter_9
  weu_11  ~ a*weu_10 + b*wFeducalter_10
  
  wFeducalter_8  ~ c*weu_7 + d*wFeducalter_7
  wFeducalter_9  ~ c*weu_8 + d*wFeducalter_8
  wFeducalter_10  ~ c*weu_9 + d*wFeducalter_9
  wFeducalter_11  ~ c*weu_10 + d*wFeducalter_10
  
  # Estimate the covariance at the first wave. 
  weu_7 ~~ wFeducalter_7 # Covariance

  # Estimate the covariances between the residuals
  weu_8 ~~ wFeducalter_8
  weu_9 ~~ wFeducalter_9
  weu_10 ~~ wFeducalter_10
  weu_11 ~~ wFeducalter_11
  
  # Estimate the variance 
  weu_7 ~~ weu_7 
  wFeducalter_7 ~~ wFeducalter_7
  
  # Estimate the residual variance
  weu_8 ~~ weu_8 
  wFeducalter_8 ~~ wFeducalter_8
  weu_9 ~~ weu_9 
  wFeducalter_9 ~~ wFeducalter_9
  weu_10 ~~ weu_10 
  wFeducalter_10 ~~ wFeducalter_10
  weu_11 ~~ weu_11 
  wFeducalter_11 ~~ wFeducalter_11
  
  # Estimate the variance and covariance of the random intercepts. 
  RIx ~~ RIx
  RIy ~~ RIy
  RIx ~~ RIy
  
  #intercepts
  Feducalter_7 ~ 1
  Feducalter_8 ~ 1
  Feducalter_9 ~ 1
  Feducalter_10 ~ 1
  Feducalter_11 ~ 1
  
  eu_7 ~ 1
  eu_8 ~ 1
  eu_9 ~ 1
  eu_10 ~ 1
  eu_11 ~ 1
  
  
'



fit <- lavaan(myModel, data = datalwb, missing = 'ML', meanstructure = T, int.ov.free = T)
summary(fit, standardized = T)

#> lavaan 0.6-7 ended normally after 34 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of free parameters                         44
#>   Number of equality constraints                    12
#>                                                       
#>   Number of observations                          2575
#>   Number of missing patterns                         2
#>                                                       
#> Model Test User Model:
#>                                                       
#>   Test statistic                                91.502
#>   Degrees of freedom                                33
#>   P-value (Chi-square)                           0.000
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Observed
#>   Observed information based on                Hessian
#> 
#> Latent Variables:
#>                     Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   RIx =~                                                                 
#>     Feducalter_7       1.000                               0.783    0.758
#>     Feducalter_8       1.000                               0.783    0.799
#>     Feducalter_9       1.000                               0.783    0.805
#>     Feducalter_10      1.000                               0.783    0.804
#>     Feducalter_11      1.000                               0.783    0.806
#>   RIy =~                                                                 
#>     eu_7               1.000                               0.954    0.814
#>     eu_8               1.000                               0.954    0.808
#>     eu_9               1.000                               0.954    0.811
#>     eu_10              1.000                               0.954    0.805
#>     eu_11              1.000                               0.954    0.800
#>   wFeducalter_7 =~                                                       
#>     Feducalter_7       1.000                               0.672    0.652
#>   wFeducalter_8 =~                                                       
#>     Feducalter_8       1.000                               0.590    0.602
#>   wFeducalter_9 =~                                                       
#>     Feducalter_9       1.000                               0.577    0.594
#>   wFeducalter_10 =~                                                      
#>     Feducalter_10      1.000                               0.578    0.594
#>   wFeducalter_11 =~                                                      
#>     Feducalter_11      1.000                               0.575    0.592
#>   weu_7 =~                                                               
#>     eu_7               1.000                               0.681    0.581
#>   weu_8 =~                                                               
#>     eu_8               1.000                               0.695    0.589
#>   weu_9 =~                                                               
#>     eu_9               1.000                               0.688    0.585
#>   weu_10 =~                                                              
#>     eu_10              1.000                               0.703    0.594
#>   weu_11 =~                                                              
#>     eu_11              1.000                               0.716    0.600
#> 
#> Regressions:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   weu_8 ~                                                               
#>     weu_7      (a)    0.135    0.015    8.835    0.000    0.133    0.133
#>     wFedcltr_7 (b)    0.024    0.015    1.590    0.112    0.023    0.023
#>   weu_9 ~                                                               
#>     weu_8      (a)    0.135    0.015    8.835    0.000    0.137    0.137
#>     wFedcltr_8 (b)    0.024    0.015    1.590    0.112    0.020    0.020
#>   weu_10 ~                                                              
#>     weu_9      (a)    0.135    0.015    8.835    0.000    0.132    0.132
#>     wFedcltr_9 (b)    0.024    0.015    1.590    0.112    0.019    0.019
#>   weu_11 ~                                                              
#>     weu_10     (a)    0.135    0.015    8.835    0.000    0.133    0.133
#>     wFdcltr_10 (b)    0.024    0.015    1.590    0.112    0.019    0.019
#>   wFeducalter_8 ~                                                       
#>     weu_7      (c)    0.023    0.011    2.082    0.037    0.027    0.027
#>     wFedcltr_7 (d)    0.073    0.014    5.132    0.000    0.083    0.083
#>   wFeducalter_9 ~                                                       
#>     weu_8      (c)    0.023    0.011    2.082    0.037    0.028    0.028
#>     wFedcltr_8 (d)    0.073    0.014    5.132    0.000    0.075    0.075
#>   wFeducalter_10 ~                                                      
#>     weu_9      (c)    0.023    0.011    2.082    0.037    0.027    0.027
#>     wFedcltr_9 (d)    0.073    0.014    5.132    0.000    0.073    0.073
#>   wFeducalter_11 ~                                                      
#>     weu_10     (c)    0.023    0.011    2.082    0.037    0.028    0.028
#>     wFdcltr_10 (d)    0.073    0.014    5.132    0.000    0.073    0.073
#> 
#> Covariances:
#>                     Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   wFeducalter_7 ~~                                                       
#>     weu_7              0.012    0.011    1.074    0.283    0.027    0.027
#>  .wFeducalter_8 ~~                                                       
#>    .weu_8              0.002    0.010    0.174    0.862    0.004    0.004
#>  .wFeducalter_9 ~~                                                       
#>    .weu_9             -0.000    0.010   -0.035    0.972   -0.001   -0.001
#>  .wFeducalter_10 ~~                                                      
#>    .weu_10             0.009    0.010    0.895    0.371    0.023    0.023
#>  .wFeducalter_11 ~~                                                      
#>    .weu_11             0.012    0.010    1.174    0.240    0.028    0.028
#>   RIx ~~                                                                 
#>     RIy                0.244    0.018   13.736    0.000    0.327    0.327
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>    .Feducalter_7     -0.003    0.021   -0.127    0.899   -0.003   -0.003
#>    .Feducalter_8      0.100    0.020    5.109    0.000    0.100    0.102
#>    .Feducalter_9      0.165    0.019    8.499    0.000    0.165    0.170
#>    .Feducalter_10     0.260    0.019   13.380    0.000    0.260    0.268
#>    .Feducalter_11     0.214    0.019   11.002    0.000    0.214    0.220
#>    .eu_7              1.263    0.023   54.683    0.000    1.263    1.078
#>    .eu_8              1.325    0.023   56.992    0.000    1.325    1.123
#>    .eu_9              1.272    0.023   54.884    0.000    1.272    1.082
#>    .eu_10             1.419    0.023   60.774    0.000    1.419    1.198
#>    .eu_11             1.512    0.023   64.362    0.000    1.512    1.268
#>     RIx               0.000                               0.000    0.000
#>     RIy               0.000                               0.000    0.000
#>     wFeducalter_7     0.000                               0.000    0.000
#>    .wFeducalter_8     0.000                               0.000    0.000
#>    .wFeducalter_9     0.000                               0.000    0.000
#>    .wFeducalter_10    0.000                               0.000    0.000
#>    .wFeducalter_11    0.000                               0.000    0.000
#>     weu_7             0.000                               0.000    0.000
#>    .weu_8             0.000                               0.000    0.000
#>    .weu_9             0.000                               0.000    0.000
#>    .weu_10            0.000                               0.000    0.000
#>    .weu_11            0.000                               0.000    0.000
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     weu_7             0.464    0.017   27.564    0.000    1.000    1.000
#>     wFeducalter_7     0.452    0.015   29.552    0.000    1.000    1.000
#>    .weu_8             0.474    0.017   28.238    0.000    0.982    0.982
#>    .wFeducalter_8     0.345    0.012   27.662    0.000    0.992    0.992
#>    .weu_9             0.464    0.016   28.618    0.000    0.981    0.981
#>    .wFeducalter_9     0.331    0.012   27.724    0.000    0.994    0.994
#>    .weu_10            0.486    0.017   28.672    0.000    0.982    0.982
#>    .wFeducalter_10    0.332    0.012   27.593    0.000    0.994    0.994
#>    .weu_11            0.503    0.017   30.154    0.000    0.982    0.982
#>    .wFeducalter_11    0.328    0.011   28.650    0.000    0.994    0.994
#>     RIx               0.612    0.020   30.827    0.000    1.000    1.000
#>     RIy               0.909    0.029   31.333    0.000    1.000    1.000
#>    .Feducalter_7      0.000                               0.000    0.000
#>    .Feducalter_8      0.000                               0.000    0.000
#>    .Feducalter_9      0.000                               0.000    0.000
#>    .Feducalter_10     0.000                               0.000    0.000
#>    .Feducalter_11     0.000                               0.000    0.000
#>    .eu_7              0.000                               0.000    0.000
#>    .eu_8              0.000                               0.000    0.000
#>    .eu_9              0.000                               0.000    0.000
#>    .eu_10             0.000                               0.000    0.000
#>    .eu_11             0.000                               0.000    0.000

---

educego included

myModel <- '

  # Create between components (random intercepts)
  RIx =~ 1*Feducalter_7 + 1*Feducalter_8 + 1*Feducalter_9 + 1*Feducalter_10 + 1*Feducalter_11
  RIy =~ 1*eu_7 + 1*eu_8 + 1*eu_9 + 1*eu_10 + 1*eu_11

  # Regression of random intercepts on z1. 
  RIx + RIy ~ educego_7   

   # Create within-person centered variables. 
  wFeducalter_7 =~ 1*Feducalter_7
  wFeducalter_8 =~ 1*Feducalter_8
  wFeducalter_9 =~ 1*Feducalter_9
  wFeducalter_10 =~ 1*Feducalter_10
  wFeducalter_11 =~ 1*Feducalter_11
  weu_7 =~ 1*eu_7
  weu_8 =~ 1*eu_8
  weu_9 =~ 1*eu_9
  weu_10 =~ 1*eu_10
  weu_11 =~ 1*eu_11 
  
  # Estimate the lagged effects (constrained)
  weu_8   ~ a*weu_7 + b*wFeducalter_7
  weu_9   ~ a*weu_8 + b*wFeducalter_8
  weu_10  ~ a*weu_9 + b*wFeducalter_9
  weu_11  ~ a*weu_10 + b*wFeducalter_10
  
  wFeducalter_8  ~ c*weu_7 + d*wFeducalter_7
  wFeducalter_9  ~ c*weu_8 + d*wFeducalter_8
  wFeducalter_10  ~ c*weu_9 + d*wFeducalter_9
  wFeducalter_11  ~ c*weu_10 + d*wFeducalter_10
  
  # Estimate the covariance at the first wave. 
  weu_7 ~~ wFeducalter_7 # Covariance

  # Estimate the covariances between the residuals
  weu_8 ~~ wFeducalter_8
  weu_9 ~~ wFeducalter_9
  weu_10 ~~ wFeducalter_10
  weu_11 ~~ wFeducalter_11
  
  # Estimate the variance 
  weu_7 ~~ weu_7 
  wFeducalter_7 ~~ wFeducalter_7
  
  # Estimate the residual variance
  weu_8 ~~ weu_8 
  wFeducalter_8 ~~ wFeducalter_8
  weu_9 ~~ weu_9 
  wFeducalter_9 ~~ wFeducalter_9
  weu_10 ~~ weu_10 
  wFeducalter_10 ~~ wFeducalter_10
  weu_11 ~~ weu_11 
  wFeducalter_11 ~~ wFeducalter_11
  
  # Estimate the variance and covariance of the random intercepts. 
  RIx ~~ RIx
  RIy ~~ RIy
  RIx ~~ RIy
  
  #intercepts
  Feducalter_7 ~ 1
  Feducalter_8 ~ 1
  Feducalter_9 ~ 1
  Feducalter_10 ~ 1
  Feducalter_11 ~ 1
  
  eu_7 ~ 1
  eu_8 ~ 1
  eu_9 ~ 1
  eu_10 ~ 1
  eu_11 ~ 1
  
  
'



fit <- lavaan(myModel, data = datalwb, missing = 'ML', meanstructure = T, int.ov.free = T)
summary(fit, standardized = T)

#> lavaan 0.6-7 ended normally after 44 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of free parameters                         46
#>   Number of equality constraints                    12
#>                                                       
#>   Number of observations                          2575
#>   Number of missing patterns                         2
#>                                                       
#> Model Test User Model:
#>                                                       
#>   Test statistic                               121.628
#>   Degrees of freedom                                41
#>   P-value (Chi-square)                           0.000
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Observed
#>   Observed information based on                Hessian
#> 
#> Latent Variables:
#>                     Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   RIx =~                                                                 
#>     Feducalter_7       1.000                               0.783    0.761
#>     Feducalter_8       1.000                               0.783    0.799
#>     Feducalter_9       1.000                               0.783    0.805
#>     Feducalter_10      1.000                               0.783    0.804
#>     Feducalter_11      1.000                               0.783    0.804
#>   RIy =~                                                                 
#>     eu_7               1.000                               0.953    0.814
#>     eu_8               1.000                               0.953    0.808
#>     eu_9               1.000                               0.953    0.810
#>     eu_10              1.000                               0.953    0.804
#>     eu_11              1.000                               0.953    0.800
#>   wFeducalter_7 =~                                                       
#>     Feducalter_7       1.000                               0.668    0.649
#>   wFeducalter_8 =~                                                       
#>     Feducalter_8       1.000                               0.589    0.601
#>   wFeducalter_9 =~                                                       
#>     Feducalter_9       1.000                               0.577    0.594
#>   wFeducalter_10 =~                                                      
#>     Feducalter_10      1.000                               0.580    0.595
#>   wFeducalter_11 =~                                                      
#>     Feducalter_11      1.000                               0.578    0.594
#>   weu_7 =~                                                               
#>     eu_7               1.000                               0.681    0.581
#>   weu_8 =~                                                               
#>     eu_8               1.000                               0.695    0.589
#>   weu_9 =~                                                               
#>     eu_9               1.000                               0.689    0.586
#>   weu_10 =~                                                              
#>     eu_10              1.000                               0.704    0.594
#>   weu_11 =~                                                              
#>     eu_11              1.000                               0.715    0.600
#> 
#> Regressions:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   RIx ~                                                                 
#>     educego_7         0.217    0.010   21.488    0.000    0.277    0.421
#>   RIy ~                                                                 
#>     educego_7         0.171    0.013   13.389    0.000    0.179    0.272
#>   weu_8 ~                                                               
#>     weu_7      (a)    0.137    0.015    8.894    0.000    0.134    0.134
#>     wFedcltr_7 (b)    0.025    0.015    1.661    0.097    0.024    0.024
#>   weu_9 ~                                                               
#>     weu_8      (a)    0.137    0.015    8.894    0.000    0.138    0.138
#>     wFedcltr_8 (b)    0.025    0.015    1.661    0.097    0.021    0.021
#>   weu_10 ~                                                              
#>     weu_9      (a)    0.137    0.015    8.894    0.000    0.134    0.134
#>     wFedcltr_9 (b)    0.025    0.015    1.661    0.097    0.020    0.020
#>   weu_11 ~                                                              
#>     weu_10     (a)    0.137    0.015    8.894    0.000    0.134    0.134
#>     wFdcltr_10 (b)    0.025    0.015    1.661    0.097    0.020    0.020
#>   wFeducalter_8 ~                                                       
#>     weu_7      (c)    0.025    0.011    2.264    0.024    0.029    0.029
#>     wFedcltr_7 (d)    0.073    0.014    5.110    0.000    0.083    0.083
#>   wFeducalter_9 ~                                                       
#>     weu_8      (c)    0.025    0.011    2.264    0.024    0.030    0.030
#>     wFedcltr_8 (d)    0.073    0.014    5.110    0.000    0.075    0.075
#>   wFeducalter_10 ~                                                      
#>     weu_9      (c)    0.025    0.011    2.264    0.024    0.030    0.030
#>     wFedcltr_9 (d)    0.073    0.014    5.110    0.000    0.073    0.073
#>   wFeducalter_11 ~                                                      
#>     weu_10     (c)    0.025    0.011    2.264    0.024    0.031    0.031
#>     wFdcltr_10 (d)    0.073    0.014    5.110    0.000    0.073    0.073
#> 
#> Covariances:
#>                     Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   wFeducalter_7 ~~                                                       
#>     weu_7              0.009    0.011    0.811    0.417    0.020    0.020
#>  .wFeducalter_8 ~~                                                       
#>    .weu_8              0.003    0.010    0.254    0.800    0.006    0.006
#>  .wFeducalter_9 ~~                                                       
#>    .weu_9              0.001    0.010    0.077    0.939    0.002    0.002
#>  .wFeducalter_10 ~~                                                      
#>    .weu_10             0.011    0.010    1.089    0.276    0.028    0.028
#>  .wFeducalter_11 ~~                                                      
#>    .weu_11             0.012    0.010    1.185    0.236    0.029    0.029
#>  .RIx ~~                                                                 
#>    .RIy                0.158    0.016   10.133    0.000    0.242    0.242
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>    .Feducalter_7     -0.835    0.043  -19.231    0.000   -0.835   -0.811
#>    .Feducalter_8     -0.732    0.043  -17.043    0.000   -0.732   -0.747
#>    .Feducalter_9     -0.667    0.043  -15.548    0.000   -0.667   -0.686
#>    .Feducalter_10    -0.572    0.043  -13.326    0.000   -0.572   -0.587
#>    .Feducalter_11    -0.618    0.043  -14.418    0.000   -0.618   -0.635
#>    .eu_7              0.610    0.054   11.352    0.000    0.610    0.521
#>    .eu_8              0.672    0.054   12.492    0.000    0.672    0.570
#>    .eu_9              0.619    0.054   11.510    0.000    0.619    0.526
#>    .eu_10             0.766    0.054   14.228    0.000    0.766    0.646
#>    .eu_11             0.859    0.054   15.942    0.000    0.859    0.721
#>    .RIx               0.000                               0.000    0.000
#>    .RIy               0.000                               0.000    0.000
#>     wFeducalter_7     0.000                               0.000    0.000
#>    .wFeducalter_8     0.000                               0.000    0.000
#>    .wFeducalter_9     0.000                               0.000    0.000
#>    .wFeducalter_10    0.000                               0.000    0.000
#>    .wFeducalter_11    0.000                               0.000    0.000
#>     weu_7             0.000                               0.000    0.000
#>    .weu_8             0.000                               0.000    0.000
#>    .weu_9             0.000                               0.000    0.000
#>    .weu_10            0.000                               0.000    0.000
#>    .weu_11            0.000                               0.000    0.000
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     weu_7             0.463    0.017   27.568    0.000    1.000    1.000
#>     wFeducalter_7     0.446    0.015   29.605    0.000    1.000    1.000
#>    .weu_8             0.474    0.017   28.253    0.000    0.981    0.981
#>    .wFeducalter_8     0.344    0.012   27.680    0.000    0.992    0.992
#>    .weu_9             0.466    0.016   28.658    0.000    0.980    0.980
#>    .wFeducalter_9     0.331    0.012   27.851    0.000    0.993    0.993
#>    .weu_10            0.487    0.017   28.709    0.000    0.982    0.982
#>    .wFeducalter_10    0.334    0.012   27.770    0.000    0.994    0.994
#>    .weu_11            0.502    0.017   30.175    0.000    0.981    0.981
#>    .wFeducalter_11    0.332    0.011   28.870    0.000    0.994    0.994
#>    .RIx               0.504    0.017   29.939    0.000    0.823    0.823
#>    .RIy               0.842    0.027   30.959    0.000    0.926    0.926
#>    .Feducalter_7      0.000                               0.000    0.000
#>    .Feducalter_8      0.000                               0.000    0.000
#>    .Feducalter_9      0.000                               0.000    0.000
#>    .Feducalter_10     0.000                               0.000    0.000
#>    .Feducalter_11     0.000                               0.000    0.000
#>    .eu_7              0.000                               0.000    0.000
#>    .eu_8              0.000                               0.000    0.000
#>    .eu_9              0.000                               0.000    0.000
#>    .eu_10             0.000                               0.000    0.000
#>    .eu_11             0.000                               0.000    0.000

---

constrained vs unconstrained model

with constrained on cross-lagged effects

myModel <- '

  # Create between components (random intercepts)
  RIx =~ 1*Feducalter_7 + 1*Feducalter_8 + 1*Feducalter_9 + 1*Feducalter_10 + 1*Feducalter_11
  RIy =~ 1*eu_7 + 1*eu_8 + 1*eu_9 + 1*eu_10 + 1*eu_11

  # Regression of random intercepts on z1. 
  RIx + RIy ~ educego_7   

   # Create within-person centered variables. 
  wFeducalter_7 =~ 1*Feducalter_7
  wFeducalter_8 =~ 1*Feducalter_8
  wFeducalter_9 =~ 1*Feducalter_9
  wFeducalter_10 =~ 1*Feducalter_10
  wFeducalter_11 =~ 1*Feducalter_11
  weu_7 =~ 1*eu_7
  weu_8 =~ 1*eu_8
  weu_9 =~ 1*eu_9
  weu_10 =~ 1*eu_10
  weu_11 =~ 1*eu_11 
  
  # Estimate the lagged effects (constrained)
  weu_8   ~ a*weu_7 + b*wFeducalter_7
  weu_9   ~ a*weu_8 + b*wFeducalter_8
  weu_10  ~ a*weu_9 + b*wFeducalter_9
  weu_11  ~ a*weu_10 + b*wFeducalter_10
  
  wFeducalter_8  ~ c*weu_7 + d*wFeducalter_7
  wFeducalter_9  ~ c*weu_8 + d*wFeducalter_8
  wFeducalter_10  ~ c*weu_9 + d*wFeducalter_9
  wFeducalter_11  ~ c*weu_10 + d*wFeducalter_10
  
  # Estimate the covariance at the first wave. 
  weu_7 ~~ wFeducalter_7 # Covariance

  # Estimate the covariances between the residuals
  weu_8 ~~ wFeducalter_8
  weu_9 ~~ wFeducalter_9
  weu_10 ~~ wFeducalter_10
  weu_11 ~~ wFeducalter_11
  
  # Estimate the variance 
  weu_7 ~~ weu_7 
  wFeducalter_7 ~~ wFeducalter_7
  
  # Estimate the residual variance
  weu_8 ~~ weu_8 
  wFeducalter_8 ~~ wFeducalter_8
  weu_9 ~~ weu_9 
  wFeducalter_9 ~~ wFeducalter_9
  weu_10 ~~ weu_10 
  wFeducalter_10 ~~ wFeducalter_10
  weu_11 ~~ weu_11 
  wFeducalter_11 ~~ wFeducalter_11
  
  # Estimate the variance and covariance of the random intercepts. 
  RIx ~~ RIx
  RIy ~~ RIy
  RIx ~~ RIy
  
  #intercepts
  Feducalter_7 ~ 1
  Feducalter_8 ~ 1
  Feducalter_9 ~ 1
  Feducalter_10 ~ 1
  Feducalter_11 ~ 1
  
  eu_7 ~ 1
  eu_8 ~ 1
  eu_9 ~ 1
  eu_10 ~ 1
  eu_11 ~ 1
  
  
'



fit <- lavaan(myModel, data = datalwb, missing = 'ML', meanstructure = T, int.ov.free = T)
summary(fit, standardized = T)

#> lavaan 0.6-7 ended normally after 44 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of free parameters                         46
#>   Number of equality constraints                    12
#>                                                       
#>   Number of observations                          2575
#>   Number of missing patterns                         2
#>                                                       
#> Model Test User Model:
#>                                                       
#>   Test statistic                               121.628
#>   Degrees of freedom                                41
#>   P-value (Chi-square)                           0.000
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Observed
#>   Observed information based on                Hessian
#> 
#> Latent Variables:
#>                     Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   RIx =~                                                                 
#>     Feducalter_7       1.000                               0.783    0.761
#>     Feducalter_8       1.000                               0.783    0.799
#>     Feducalter_9       1.000                               0.783    0.805
#>     Feducalter_10      1.000                               0.783    0.804
#>     Feducalter_11      1.000                               0.783    0.804
#>   RIy =~                                                                 
#>     eu_7               1.000                               0.953    0.814
#>     eu_8               1.000                               0.953    0.808
#>     eu_9               1.000                               0.953    0.810
#>     eu_10              1.000                               0.953    0.804
#>     eu_11              1.000                               0.953    0.800
#>   wFeducalter_7 =~                                                       
#>     Feducalter_7       1.000                               0.668    0.649
#>   wFeducalter_8 =~                                                       
#>     Feducalter_8       1.000                               0.589    0.601
#>   wFeducalter_9 =~                                                       
#>     Feducalter_9       1.000                               0.577    0.594
#>   wFeducalter_10 =~                                                      
#>     Feducalter_10      1.000                               0.580    0.595
#>   wFeducalter_11 =~                                                      
#>     Feducalter_11      1.000                               0.578    0.594
#>   weu_7 =~                                                               
#>     eu_7               1.000                               0.681    0.581
#>   weu_8 =~                                                               
#>     eu_8               1.000                               0.695    0.589
#>   weu_9 =~                                                               
#>     eu_9               1.000                               0.689    0.586
#>   weu_10 =~                                                              
#>     eu_10              1.000                               0.704    0.594
#>   weu_11 =~                                                              
#>     eu_11              1.000                               0.715    0.600
#> 
#> Regressions:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   RIx ~                                                                 
#>     educego_7         0.217    0.010   21.488    0.000    0.277    0.421
#>   RIy ~                                                                 
#>     educego_7         0.171    0.013   13.389    0.000    0.179    0.272
#>   weu_8 ~                                                               
#>     weu_7      (a)    0.137    0.015    8.894    0.000    0.134    0.134
#>     wFedcltr_7 (b)    0.025    0.015    1.661    0.097    0.024    0.024
#>   weu_9 ~                                                               
#>     weu_8      (a)    0.137    0.015    8.894    0.000    0.138    0.138
#>     wFedcltr_8 (b)    0.025    0.015    1.661    0.097    0.021    0.021
#>   weu_10 ~                                                              
#>     weu_9      (a)    0.137    0.015    8.894    0.000    0.134    0.134
#>     wFedcltr_9 (b)    0.025    0.015    1.661    0.097    0.020    0.020
#>   weu_11 ~                                                              
#>     weu_10     (a)    0.137    0.015    8.894    0.000    0.134    0.134
#>     wFdcltr_10 (b)    0.025    0.015    1.661    0.097    0.020    0.020
#>   wFeducalter_8 ~                                                       
#>     weu_7      (c)    0.025    0.011    2.264    0.024    0.029    0.029
#>     wFedcltr_7 (d)    0.073    0.014    5.110    0.000    0.083    0.083
#>   wFeducalter_9 ~                                                       
#>     weu_8      (c)    0.025    0.011    2.264    0.024    0.030    0.030
#>     wFedcltr_8 (d)    0.073    0.014    5.110    0.000    0.075    0.075
#>   wFeducalter_10 ~                                                      
#>     weu_9      (c)    0.025    0.011    2.264    0.024    0.030    0.030
#>     wFedcltr_9 (d)    0.073    0.014    5.110    0.000    0.073    0.073
#>   wFeducalter_11 ~                                                      
#>     weu_10     (c)    0.025    0.011    2.264    0.024    0.031    0.031
#>     wFdcltr_10 (d)    0.073    0.014    5.110    0.000    0.073    0.073
#> 
#> Covariances:
#>                     Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   wFeducalter_7 ~~                                                       
#>     weu_7              0.009    0.011    0.811    0.417    0.020    0.020
#>  .wFeducalter_8 ~~                                                       
#>    .weu_8              0.003    0.010    0.254    0.800    0.006    0.006
#>  .wFeducalter_9 ~~                                                       
#>    .weu_9              0.001    0.010    0.077    0.939    0.002    0.002
#>  .wFeducalter_10 ~~                                                      
#>    .weu_10             0.011    0.010    1.089    0.276    0.028    0.028
#>  .wFeducalter_11 ~~                                                      
#>    .weu_11             0.012    0.010    1.185    0.236    0.029    0.029
#>  .RIx ~~                                                                 
#>    .RIy                0.158    0.016   10.133    0.000    0.242    0.242
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>    .Feducalter_7     -0.835    0.043  -19.231    0.000   -0.835   -0.811
#>    .Feducalter_8     -0.732    0.043  -17.043    0.000   -0.732   -0.747
#>    .Feducalter_9     -0.667    0.043  -15.548    0.000   -0.667   -0.686
#>    .Feducalter_10    -0.572    0.043  -13.326    0.000   -0.572   -0.587
#>    .Feducalter_11    -0.618    0.043  -14.418    0.000   -0.618   -0.635
#>    .eu_7              0.610    0.054   11.352    0.000    0.610    0.521
#>    .eu_8              0.672    0.054   12.492    0.000    0.672    0.570
#>    .eu_9              0.619    0.054   11.510    0.000    0.619    0.526
#>    .eu_10             0.766    0.054   14.228    0.000    0.766    0.646
#>    .eu_11             0.859    0.054   15.942    0.000    0.859    0.721
#>    .RIx               0.000                               0.000    0.000
#>    .RIy               0.000                               0.000    0.000
#>     wFeducalter_7     0.000                               0.000    0.000
#>    .wFeducalter_8     0.000                               0.000    0.000
#>    .wFeducalter_9     0.000                               0.000    0.000
#>    .wFeducalter_10    0.000                               0.000    0.000
#>    .wFeducalter_11    0.000                               0.000    0.000
#>     weu_7             0.000                               0.000    0.000
#>    .weu_8             0.000                               0.000    0.000
#>    .weu_9             0.000                               0.000    0.000
#>    .weu_10            0.000                               0.000    0.000
#>    .weu_11            0.000                               0.000    0.000
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     weu_7             0.463    0.017   27.568    0.000    1.000    1.000
#>     wFeducalter_7     0.446    0.015   29.605    0.000    1.000    1.000
#>    .weu_8             0.474    0.017   28.253    0.000    0.981    0.981
#>    .wFeducalter_8     0.344    0.012   27.680    0.000    0.992    0.992
#>    .weu_9             0.466    0.016   28.658    0.000    0.980    0.980
#>    .wFeducalter_9     0.331    0.012   27.851    0.000    0.993    0.993
#>    .weu_10            0.487    0.017   28.709    0.000    0.982    0.982
#>    .wFeducalter_10    0.334    0.012   27.770    0.000    0.994    0.994
#>    .weu_11            0.502    0.017   30.175    0.000    0.981    0.981
#>    .wFeducalter_11    0.332    0.011   28.870    0.000    0.994    0.994
#>    .RIx               0.504    0.017   29.939    0.000    0.823    0.823
#>    .RIy               0.842    0.027   30.959    0.000    0.926    0.926
#>    .Feducalter_7      0.000                               0.000    0.000
#>    .Feducalter_8      0.000                               0.000    0.000
#>    .Feducalter_9      0.000                               0.000    0.000
#>    .Feducalter_10     0.000                               0.000    0.000
#>    .Feducalter_11     0.000                               0.000    0.000
#>    .eu_7              0.000                               0.000    0.000
#>    .eu_8              0.000                               0.000    0.000
#>    .eu_9              0.000                               0.000    0.000
#>    .eu_10             0.000                               0.000    0.000
#>    .eu_11             0.000                               0.000    0.000

---

without constrained on cross-lagged effects

myModel <- '

  # Create between components (random intercepts)
  RIx =~ 1*Feducalter_7 + 1*Feducalter_8 + 1*Feducalter_9 + 1*Feducalter_10 + 1*Feducalter_11
  RIy =~ 1*eu_7 + 1*eu_8 + 1*eu_9 + 1*eu_10 + 1*eu_11

  # Regression of random intercepts on z1. 
  RIx + RIy ~ educego_7   

   # Create within-person centered variables. 
  wFeducalter_7 =~ 1*Feducalter_7
  wFeducalter_8 =~ 1*Feducalter_8
  wFeducalter_9 =~ 1*Feducalter_9
  wFeducalter_10 =~ 1*Feducalter_10
  wFeducalter_11 =~ 1*Feducalter_11
  weu_7 =~ 1*eu_7
  weu_8 =~ 1*eu_8
  weu_9 =~ 1*eu_9
  weu_10 =~ 1*eu_10
  weu_11 =~ 1*eu_11 
  
  # Estimate the lagged effects (constrained)
  weu_8   ~ weu_7 + wFeducalter_7
  weu_9   ~ weu_8 + wFeducalter_8
  weu_10  ~ weu_9 + wFeducalter_9
  weu_11  ~ weu_10 + wFeducalter_10
  
  wFeducalter_8  ~ weu_7 + wFeducalter_7
  wFeducalter_9  ~ weu_8 + wFeducalter_8
  wFeducalter_10  ~ weu_9 + wFeducalter_9
  wFeducalter_11  ~ weu_10 + wFeducalter_10
  
  # Estimate the covariance at the first wave. 
  weu_7 ~~ wFeducalter_7 # Covariance

  # Estimate the covariances between the residuals
  weu_8 ~~ wFeducalter_8
  weu_9 ~~ wFeducalter_9
  weu_10 ~~ wFeducalter_10
  weu_11 ~~ wFeducalter_11
  
  # Estimate the variance 
  weu_7 ~~ weu_7 
  wFeducalter_7 ~~ wFeducalter_7
  
  # Estimate the residual variance
  weu_8 ~~ weu_8 
  wFeducalter_8 ~~ wFeducalter_8
  weu_9 ~~ weu_9 
  wFeducalter_9 ~~ wFeducalter_9
  weu_10 ~~ weu_10 
  wFeducalter_10 ~~ wFeducalter_10
  weu_11 ~~ weu_11 
  wFeducalter_11 ~~ wFeducalter_11
  
  # Estimate the variance and covariance of the random intercepts. 
  RIx ~~ RIx
  RIy ~~ RIy
  RIx ~~ RIy
  
  #intercepts
  Feducalter_7 ~ 1
  Feducalter_8 ~ 1
  Feducalter_9 ~ 1
  Feducalter_10 ~ 1
  Feducalter_11 ~ 1
  
  eu_7 ~ 1
  eu_8 ~ 1
  eu_9 ~ 1
  eu_10 ~ 1
  eu_11 ~ 1
  
  
'



fit <- lavaan(myModel, data = datalwb, missing = 'ML', meanstructure = T, int.ov.free = T)
summary(fit, standardized = T)

#> lavaan 0.6-7 ended normally after 49 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of free parameters                         46
#>                                                       
#>   Number of observations                          2575
#>   Number of missing patterns                         2
#>                                                       
#> Model Test User Model:
#>                                                       
#>   Test statistic                                94.854
#>   Degrees of freedom                                29
#>   P-value (Chi-square)                           0.000
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Observed
#>   Observed information based on                Hessian
#> 
#> Latent Variables:
#>                     Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   RIx =~                                                                 
#>     Feducalter_7       1.000                               0.784    0.768
#>     Feducalter_8       1.000                               0.784    0.808
#>     Feducalter_9       1.000                               0.784    0.807
#>     Feducalter_10      1.000                               0.784    0.798
#>     Feducalter_11      1.000                               0.784    0.796
#>   RIy =~                                                                 
#>     eu_7               1.000                               0.954    0.813
#>     eu_8               1.000                               0.954    0.808
#>     eu_9               1.000                               0.954    0.813
#>     eu_10              1.000                               0.954    0.810
#>     eu_11              1.000                               0.954    0.798
#>   wFeducalter_7 =~                                                       
#>     Feducalter_7       1.000                               0.654    0.641
#>   wFeducalter_8 =~                                                       
#>     Feducalter_8       1.000                               0.573    0.590
#>   wFeducalter_9 =~                                                       
#>     Feducalter_9       1.000                               0.574    0.591
#>   wFeducalter_10 =~                                                      
#>     Feducalter_10      1.000                               0.592    0.602
#>   wFeducalter_11 =~                                                      
#>     Feducalter_11      1.000                               0.596    0.605
#>   weu_7 =~                                                               
#>     eu_7               1.000                               0.683    0.582
#>   weu_8 =~                                                               
#>     eu_8               1.000                               0.696    0.590
#>   weu_9 =~                                                               
#>     eu_9               1.000                               0.685    0.583
#>   weu_10 =~                                                              
#>     eu_10              1.000                               0.690    0.586
#>   weu_11 =~                                                              
#>     eu_11              1.000                               0.722    0.603
#> 
#> Regressions:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   RIx ~                                                                 
#>     educego_7         0.219    0.010   21.620    0.000    0.279    0.423
#>   RIy ~                                                                 
#>     educego_7         0.170    0.013   13.338    0.000    0.178    0.271
#>   weu_8 ~                                                               
#>     weu_7             0.136    0.031    4.415    0.000    0.133    0.133
#>     wFeducalter_7     0.030    0.029    1.030    0.303    0.028    0.028
#>   weu_9 ~                                                               
#>     weu_8             0.147    0.029    5.152    0.000    0.150    0.150
#>     wFeducalter_8     0.077    0.034    2.270    0.023    0.065    0.065
#>   weu_10 ~                                                              
#>     weu_9             0.072    0.032    2.283    0.022    0.072    0.072
#>     wFeducalter_9     0.001    0.035    0.021    0.983    0.001    0.001
#>   weu_11 ~                                                              
#>     weu_10            0.162    0.030    5.318    0.000    0.155    0.155
#>     wFeducalter_10   -0.004    0.033   -0.116    0.908   -0.003   -0.003
#>   wFeducalter_8 ~                                                       
#>     weu_7             0.023    0.025    0.904    0.366    0.027    0.027
#>     wFeducalter_7     0.007    0.027    0.258    0.796    0.008    0.008
#>   wFeducalter_9 ~                                                       
#>     weu_8             0.026    0.024    1.057    0.290    0.031    0.031
#>     wFeducalter_8     0.065    0.031    2.063    0.039    0.065    0.065
#>   wFeducalter_10 ~                                                      
#>     weu_9             0.031    0.026    1.208    0.227    0.036    0.036
#>     wFeducalter_9     0.069    0.031    2.271    0.023    0.067    0.067
#>   wFeducalter_11 ~                                                      
#>     weu_10            0.029    0.024    1.225    0.221    0.034    0.034
#>     wFeducalter_10    0.154    0.029    5.357    0.000    0.152    0.152
#> 
#> Covariances:
#>                     Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   wFeducalter_7 ~~                                                       
#>     weu_7              0.009    0.012    0.744    0.457    0.021    0.021
#>  .wFeducalter_8 ~~                                                       
#>    .weu_8              0.006    0.012    0.526    0.599    0.016    0.016
#>  .wFeducalter_9 ~~                                                       
#>    .weu_9              0.005    0.011    0.428    0.669    0.012    0.012
#>  .wFeducalter_10 ~~                                                      
#>    .weu_10             0.007    0.012    0.624    0.532    0.018    0.018
#>  .wFeducalter_11 ~~                                                      
#>    .weu_11             0.011    0.011    0.991    0.322    0.025    0.025
#>  .RIx ~~                                                                 
#>    .RIy                0.156    0.016    9.993    0.000    0.239    0.239
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>    .Feducalter_7     -0.842    0.043  -19.395    0.000   -0.842   -0.824
#>    .Feducalter_8     -0.739    0.043  -17.213    0.000   -0.739   -0.761
#>    .Feducalter_9     -0.674    0.043  -15.690    0.000   -0.674   -0.693
#>    .Feducalter_10    -0.579    0.043  -13.447    0.000   -0.579   -0.589
#>    .Feducalter_11    -0.626    0.043  -14.523    0.000   -0.626   -0.635
#>    .eu_7              0.612    0.054   11.369    0.000    0.612    0.521
#>    .eu_8              0.674    0.054   12.508    0.000    0.674    0.570
#>    .eu_9              0.620    0.054   11.533    0.000    0.620    0.528
#>    .eu_10             0.768    0.054   14.262    0.000    0.768    0.652
#>    .eu_11             0.861    0.054   15.946    0.000    0.861    0.720
#>    .RIx               0.000                               0.000    0.000
#>    .RIy               0.000                               0.000    0.000
#>     wFeducalter_7     0.000                               0.000    0.000
#>    .wFeducalter_8     0.000                               0.000    0.000
#>    .wFeducalter_9     0.000                               0.000    0.000
#>    .wFeducalter_10    0.000                               0.000    0.000
#>    .wFeducalter_11    0.000                               0.000    0.000
#>     weu_7             0.000                               0.000    0.000
#>    .weu_8             0.000                               0.000    0.000
#>    .weu_9             0.000                               0.000    0.000
#>    .weu_10            0.000                               0.000    0.000
#>    .weu_11            0.000                               0.000    0.000
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     weu_7             0.466    0.019   24.250    0.000    1.000    1.000
#>     wFeducalter_7     0.428    0.016   26.970    0.000    1.000    1.000
#>    .weu_8             0.476    0.019   25.539    0.000    0.981    0.981
#>    .wFeducalter_8     0.328    0.014   22.735    0.000    0.999    0.999
#>    .weu_9             0.456    0.018   25.613    0.000    0.973    0.973
#>    .wFeducalter_9     0.328    0.013   24.552    0.000    0.995    0.995
#>    .weu_10            0.474    0.020   23.587    0.000    0.995    0.995
#>    .wFeducalter_10    0.348    0.014   24.906    0.000    0.994    0.994
#>    .weu_11            0.508    0.018   28.330    0.000    0.976    0.976
#>    .wFeducalter_11    0.347    0.013   27.648    0.000    0.975    0.975
#>    .RIx               0.505    0.017   29.717    0.000    0.821    0.821
#>    .RIy               0.844    0.027   30.932    0.000    0.927    0.927
#>    .Feducalter_7      0.000                               0.000    0.000
#>    .Feducalter_8      0.000                               0.000    0.000
#>    .Feducalter_9      0.000                               0.000    0.000
#>    .Feducalter_10     0.000                               0.000    0.000
#>    .Feducalter_11     0.000                               0.000    0.000
#>    .eu_7              0.000                               0.000    0.000
#>    .eu_8              0.000                               0.000    0.000
#>    .eu_9              0.000                               0.000    0.000
#>    .eu_10             0.000                               0.000    0.000
#>    .eu_11             0.000                               0.000    0.000

structural changes over time

this means that we no longer have a random intercept but rather a latent variable. We however know we have also structural changes. And our measures are one year apart.

myModel <- '

  # Create between components (random intercepts)
  RIx =~ 1*Feducalter_7 + Feducalter_8 + Feducalter_9 + Feducalter_10 + Feducalter_11
  RIy =~ 1*eu_7 + eu_8 + eu_9 + eu_10 + eu_11

  # Regression of random intercepts / latent variable on z1. 
  RIx + RIy ~ educego_7   

   # Create within-person centered variables. 
  wFeducalter_7 =~ 1*Feducalter_7
  wFeducalter_8 =~ 1*Feducalter_8
  wFeducalter_9 =~ 1*Feducalter_9
  wFeducalter_10 =~ 1*Feducalter_10
  wFeducalter_11 =~ 1*Feducalter_11
  weu_7 =~ 1*eu_7
  weu_8 =~ 1*eu_8
  weu_9 =~ 1*eu_9
  weu_10 =~ 1*eu_10
  weu_11 =~ 1*eu_11 
  
  # Estimate the lagged effects (constrained)
  weu_8   ~ weu_7 + wFeducalter_7
  weu_9   ~ weu_8 + wFeducalter_8
  weu_10  ~ weu_9 + wFeducalter_9
  weu_11  ~ weu_10 + wFeducalter_10
  
  wFeducalter_8  ~ weu_7 + wFeducalter_7
  wFeducalter_9  ~ weu_8 + wFeducalter_8
  wFeducalter_10  ~ weu_9 + wFeducalter_9
  wFeducalter_11  ~ weu_10 + wFeducalter_10
  
  # Estimate the covariance at the first wave. 
  weu_7 ~~ wFeducalter_7 # Covariance

  # Estimate the covariances between the residuals
  weu_8 ~~ wFeducalter_8
  weu_9 ~~ wFeducalter_9
  weu_10 ~~ wFeducalter_10
  weu_11 ~~ wFeducalter_11
  
  # Estimate the variance 
  weu_7 ~~ weu_7 
  wFeducalter_7 ~~ wFeducalter_7
  
  # Estimate the residual variance
  weu_8 ~~ weu_8 
  wFeducalter_8 ~~ wFeducalter_8
  weu_9 ~~ weu_9 
  wFeducalter_9 ~~ wFeducalter_9
  weu_10 ~~ weu_10 
  wFeducalter_10 ~~ wFeducalter_10
  weu_11 ~~ weu_11 
  wFeducalter_11 ~~ wFeducalter_11
  
  # Estimate the variance and covariance of the random intercepts. 
  RIx ~~ RIx
  RIy ~~ RIy
  RIx ~~ RIy
  
  #intercepts
  Feducalter_7 ~ 1
  Feducalter_8 ~ 1
  Feducalter_9 ~ 1
  Feducalter_10 ~ 1
  Feducalter_11 ~ 1
  
  eu_7 ~ 1
  eu_8 ~ 1
  eu_9 ~ 1
  eu_10 ~ 1
  eu_11 ~ 1
  
  
'



fit <- lavaan(myModel, data = datalwb, missing = 'ML', meanstructure = T, int.ov.free = T)
summary(fit, standardized = T)

#> lavaan 0.6-7 ended normally after 61 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of free parameters                         54
#>                                                       
#>   Number of observations                          2575
#>   Number of missing patterns                         2
#>                                                       
#> Model Test User Model:
#>                                                       
#>   Test statistic                                45.122
#>   Degrees of freedom                                21
#>   P-value (Chi-square)                           0.002
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Observed
#>   Observed information based on                Hessian
#> 
#> Latent Variables:
#>                     Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   RIx =~                                                                 
#>     Feducalter_7       1.000                               0.817    0.787
#>     Feducalter_8       0.980    0.025   39.535    0.000    0.801    0.825
#>     Feducalter_9       1.014    0.028   35.734    0.000    0.829    0.832
#>     Feducalter_10      0.948    0.028   33.597    0.000    0.775    0.788
#>     Feducalter_11      0.869    0.025   34.369    0.000    0.710    0.753
#>   RIy =~                                                                 
#>     eu_7               1.000                               0.927    0.801
#>     eu_8               1.044    0.023   46.041    0.000    0.968    0.814
#>     eu_9               1.052    0.027   38.833    0.000    0.976    0.823
#>     eu_10              1.019    0.031   32.882    0.000    0.944    0.807
#>     eu_11              1.041    0.029   35.465    0.000    0.965    0.802
#>   wFeducalter_7 =~                                                       
#>     Feducalter_7       1.000                               0.641    0.617
#>   wFeducalter_8 =~                                                       
#>     Feducalter_8       1.000                               0.548    0.565
#>   wFeducalter_9 =~                                                       
#>     Feducalter_9       1.000                               0.553    0.555
#>   wFeducalter_10 =~                                                      
#>     Feducalter_10      1.000                               0.606    0.616
#>   wFeducalter_11 =~                                                      
#>     Feducalter_11      1.000                               0.620    0.658
#>   weu_7 =~                                                               
#>     eu_7               1.000                               0.692    0.598
#>   weu_8 =~                                                               
#>     eu_8               1.000                               0.692    0.581
#>   weu_9 =~                                                               
#>     eu_9               1.000                               0.673    0.568
#>   weu_10 =~                                                              
#>     eu_10              1.000                               0.690    0.590
#>   weu_11 =~                                                              
#>     eu_11              1.000                               0.719    0.598
#> 
#> Regressions:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   RIx ~                                                                 
#>     educego_7         0.228    0.011   19.981    0.000    0.279    0.423
#>   RIy ~                                                                 
#>     educego_7         0.165    0.013   12.893    0.000    0.178    0.270
#>   weu_8 ~                                                               
#>     weu_7             0.140    0.040    3.546    0.000    0.140    0.140
#>     wFeducalter_7     0.026    0.031    0.841    0.401    0.024    0.024
#>   weu_9 ~                                                               
#>     weu_8             0.125    0.035    3.582    0.000    0.129    0.129
#>     wFeducalter_8     0.082    0.036    2.238    0.025    0.066    0.066
#>   weu_10 ~                                                              
#>     weu_9             0.058    0.040    1.428    0.153    0.056    0.056
#>     wFeducalter_9     0.005    0.037    0.131    0.896    0.004    0.004
#>   weu_11 ~                                                              
#>     weu_10            0.159    0.040    3.982    0.000    0.152    0.152
#>     wFeducalter_10    0.002    0.032    0.069    0.945    0.002    0.002
#>   wFeducalter_8 ~                                                       
#>     weu_7             0.019    0.024    0.799    0.425    0.024    0.024
#>     wFeducalter_7    -0.048    0.036   -1.332    0.183   -0.056   -0.056
#>   wFeducalter_9 ~                                                       
#>     weu_8             0.023    0.026    0.904    0.366    0.029    0.029
#>     wFeducalter_8    -0.015    0.039   -0.380    0.704   -0.015   -0.015
#>   wFeducalter_10 ~                                                      
#>     weu_9             0.035    0.027    1.316    0.188    0.039    0.039
#>     wFeducalter_9     0.068    0.042    1.615    0.106    0.062    0.062
#>   wFeducalter_11 ~                                                      
#>     weu_10            0.030    0.022    1.335    0.182    0.033    0.033
#>     wFeducalter_10    0.214    0.029    7.316    0.000    0.209    0.209
#> 
#> Covariances:
#>                     Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>   wFeducalter_7 ~~                                                       
#>     weu_7              0.006    0.012    0.510    0.610    0.014    0.014
#>  .wFeducalter_8 ~~                                                       
#>    .weu_8              0.004    0.012    0.341    0.733    0.011    0.011
#>  .wFeducalter_9 ~~                                                       
#>    .weu_9              0.007    0.011    0.631    0.528    0.020    0.020
#>  .wFeducalter_10 ~~                                                      
#>    .weu_10             0.010    0.012    0.828    0.408    0.024    0.024
#>  .wFeducalter_11 ~~                                                      
#>    .weu_11             0.013    0.010    1.211    0.226    0.029    0.029
#>  .RIx ~~                                                                 
#>    .RIy                0.155    0.016    9.620    0.000    0.234    0.234
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>    .Feducalter_7     -0.877    0.048  -18.271    0.000   -0.877   -0.845
#>    .Feducalter_8     -0.757    0.046  -16.474    0.000   -0.757   -0.780
#>    .Feducalter_9     -0.721    0.046  -15.581    0.000   -0.721   -0.724
#>    .Feducalter_10    -0.569    0.045  -12.721    0.000   -0.569   -0.578
#>    .Feducalter_11    -0.545    0.042  -13.090    0.000   -0.545   -0.579
#>    .eu_7              0.632    0.054   11.749    0.000    0.632    0.546
#>    .eu_8              0.666    0.056   11.917    0.000    0.666    0.560
#>    .eu_9              0.608    0.055   10.948    0.000    0.608    0.513
#>    .eu_10             0.776    0.054   14.324    0.000    0.776    0.663
#>    .eu_11             0.855    0.056   15.401    0.000    0.855    0.710
#>    .RIx               0.000                               0.000    0.000
#>    .RIy               0.000                               0.000    0.000
#>     wFeducalter_7     0.000                               0.000    0.000
#>    .wFeducalter_8     0.000                               0.000    0.000
#>    .wFeducalter_9     0.000                               0.000    0.000
#>    .wFeducalter_10    0.000                               0.000    0.000
#>    .wFeducalter_11    0.000                               0.000    0.000
#>     weu_7             0.000                               0.000    0.000
#>    .weu_8             0.000                               0.000    0.000
#>    .weu_9             0.000                               0.000    0.000
#>    .weu_10            0.000                               0.000    0.000
#>    .weu_11            0.000                               0.000    0.000
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
#>     weu_7             0.479    0.023   21.010    0.000    1.000    1.000
#>     wFeducalter_7     0.410    0.018   22.270    0.000    1.000    1.000
#>    .weu_8             0.468    0.023   20.197    0.000    0.980    0.980
#>    .wFeducalter_8     0.299    0.019   15.697    0.000    0.996    0.996
#>    .weu_9             0.443    0.020   21.708    0.000    0.979    0.979
#>    .wFeducalter_9     0.305    0.017   18.147    0.000    0.999    0.999
#>    .weu_10            0.475    0.026   18.176    0.000    0.997    0.997
#>    .wFeducalter_10    0.365    0.016   22.518    0.000    0.995    0.995
#>    .weu_11            0.506    0.020   24.704    0.000    0.977    0.977
#>    .wFeducalter_11    0.367    0.012   30.045    0.000    0.955    0.955
#>    .RIx               0.548    0.026   21.099    0.000    0.821    0.821
#>    .RIy               0.797    0.036   21.861    0.000    0.927    0.927
#>    .Feducalter_7      0.000                               0.000    0.000
#>    .Feducalter_8      0.000                               0.000    0.000
#>    .Feducalter_9      0.000                               0.000    0.000
#>    .Feducalter_10     0.000                               0.000    0.000
#>    .Feducalter_11     0.000                               0.000    0.000
#>    .eu_7              0.000                               0.000    0.000
#>    .eu_8              0.000                               0.000    0.000
#>    .eu_9              0.000                               0.000    0.000
#>    .eu_10             0.000                               0.000    0.000
#>    .eu_11             0.000                               0.000    0.000

---

References

Hamaker, Ellen L, Rebecca M Kuiper, and Raoul PPP Grasman. 2015. “A Critique of the Cross-Lagged Panel Model.” Psychological Methods 20 (1): 102.

Mulder, Jeroen D., and Ellen L. Hamaker. 2020. “Three Extensions of the Random Intercept Cross-Lagged Panel Model.” Structural Equation Modeling: A Multidisciplinary Journal. https://doi.org/10.1080/10705511.2020.1784738.

Rosseel, Yves. 2012. “lavaan: An R Package for Structural Equation Modeling.” Journal of Statistical Software 48 (2): 1–36. http://www.jstatsoft.org/v48/i02/.