Estimation of parameters via Robbins-Monro algorithm

ts_estim is the workhorse function of the package RsienaTwoStep. For details on the simulation function see ts_sims(). This function aims to estimate the model parameters according to the Robbins-Monro algorithm as described in (Snijders 2001) .

Usage

ts_estim(
  ans = NULL,
  mydata = NULL,
  myeff = NULL,
  startvalues = NULL,
  net1 = NULL,
  net2 = NULL,
  ccovar = NULL,
  statistics = NULL,
  b = 0.5,
  conv = 0.001,
  nite = 1000,
  itef1 = 50,
  itef3 = 1000,
  p2step = c(1, 0, 0),
  dist1 = NULL,
  dist2 = NULL,
  modet1 = "degree",
  modet2 = "degree",
  verbose = TRUE,
  parallel = FALSE,
  returnDeps = FALSE,
  phase1 = TRUE,
  phase3 = TRUE
)

ts_targets(
  ans = NULL,
  mydata = NULL,
  myeff = NULL,
  net1 = NULL,
  net2 = NULL,
  ccovar = NULL,
  statistics = NULL
)

ts_phase1(
  ans = NULL,
  mydata = NULL,
  myeff = NULL,
  net1 = NULL,
  net2 = NULL,
  ccovar = NULL,
  statistics = NULL,
  itef1 = 100,
  p2step = c(1, 0, 0),
  dist1 = NULL,
  dist2 = NULL,
  modet1 = NULL,
  modet2 = NULL,
  verbose = TRUE,
  parallel = FALSE
)

ts_phase3(
  ans = NULL,
  mydata = NULL,
  myeff = NULL,
  net1 = NULL,
  net2 = NULL,
  ccovar = NULL,
  statistics = NULL,
  startvalues = NULL,
  itef3 = 1000,
  p2step = c(1, 0, 0),
  dist1 = NULL,
  dist2 = NULL,
  modet1 = "degree",
  modet2 = "degree",
  verbose = TRUE,
  parallel = FALSE,
  returnDeps = FALSE
)

Arguments

ans: Results of class sienaFit, produced by a call to RSiena::siena07()
mydata: Siena data object created by a call to RSiena::sienaDataCreate()
myeff: Siena effects object created by a call to RSiena::getEffects()
startvalues: if not provided manually, taken from results of ans$theta, or if ans is not provided from summary(myeff)$initialValue.
net1: adjacency matrix, the adjacency matrix representing the relations between actors at Time=1. Valid values are 0 and 1. If not provided manually, retrieved from ans or mydata.
net2: adjacency matrix, the adjacency matrix representing the relations between actors at Time=2. Valid values are 0 and 1. If not provided manually, retrieved from ans or mydata.
ccovar: data frame with named time-constant covariates. If not provided manually, retrieved from ans or mydata.
statistics: list of statistics of RsienaTwoStep, see: ts_degree() and DETAILS. If not provided manually, retrieved from ans or myeff.
b: numeric between 0.1 and 1 (default =0.5), used in Robbins-Monro algorithm.
conv: numeric. Robbins-Monro algorithm stops if the mean deviation of parameters after each update steps become smaller than conv
nite: number of iterations phase2 (actual estimation of parameters)
itef1: number of total iterations phase1 (To get to a crude Jacobian matrix, which can be used in phase2) )
itef3: number of total iterations phase3 (To estimate SE). This phase will take the longest.
p2step: numeric vector of length 3, setting the ratio of ministep, twostep and twoministeps. This parameter is passed to ts_sims().
dist1: numeric, minimal path length between ego1 and ego2 at time1 in order to be allowed to start a cooperation. If NULL all dyads are allowed to start a cooperation. This parameter is passed to ts_sims().
dist2: numeric, minimal path length between ego1 and ego2 at time2 in order for twostep to be counted as cooperation. This parameter is passed to ts_sims().
modet1: string, indicating the type of ties being evaluated at time1. "degree" considers all ties as undirected. "outdegree" only allows directed paths starting from ego1 and ending at ego2. "indegree" only allows directed paths starting from ego2 and ending at ego2. This parameter is passed to ts_sims().
modet2: string, indicating the type of ties being evaluated at time2. "degree" considers all ties as undirected. "outdegree" only allows directed paths starting from ego1 and ending at ego2. "indegree" only allows directed paths starting from ego2 and ending at ego2. This parameter is passed to ts_sims().
verbose,: TRUE/FALSE. If set to true it shows the iteration steps and some results.
parallel: Boolean. TRUE/FALSE.
returnDeps: Boolean. If TRUE the simulated dependent variables (networks, behaviour) of phase3 will be returned.
phase1: TRUE/FALSE, If False no Jacobian matrix is calculated.
phase3: TRUE/FALSE, if FALSE no SE are calculated

Value

If phase3 = FALSE A dataframe of estimated parameters. The last row are the final solutions of the Robbins Monro algorithm. If Phase 3 = TRUE a list with first list element the data frame of estimated parameters and the second element the results of phase 3.

list, containing: estim, covtheta, tstat

tconv.max, zdevs, and if returnDeps = TRUE

simnets

Details

For examples on how to use ts_estim() see: vignette("1.Introduction_RsienaTwoStep", package="RsienaTwoStep") or the package website. Before you set parallel to TRUE make sure to set-up a cluster with the package doParallel (see Examples).

p2step==c(1,0,0): ministep
p2step==c(0,1,0) & dist1==NULL & dist2==NULL: twostep-simultaneity
p2step==c(0,1,0) & dist1!=NULL & dist2==NULL: twostep-strict coordination
p2step==c(0,1,0) & dist1!=NULL & dist2!=NULL: twostep-weak coordination
p2step==c(0,0,1): two-ministeps

References

Ripley RM, Snijders TA, Boda Z, Vörös A, Preciado P (2022). Manual for SIENA version 4.0 (version August 11, 2022). http://www.stats.ox.ac.uk/~snijders/siena/RSiena_manual.pdf. Snijders TA (2001). “The statistical evaluation of social network dynamics.” Sociological methodology, 31(1), 361--395.

Examples

if (FALSE) {
# It is good practice to check if `RsienaTwoStep` uses the same
# target values as `RSiena`, which can be retrieved like: `ans$targets`.
ts_targets(net1 = s501, net2 = s502, statistics = list(ts_degree, ts_recip))
# In normal use case you do not want to estimate the Jacobian matrix yourself
# for phase 1. We simply use the matrix from `RSiena`. Except if you really
# expect different outcomes from the twostep model and not using a
# Dinv matrix at all does not work.
# Phase 1 only
jac <- ts_phase1(net1 = s501,
 net2 = s502,
 statistics = list(ts_degree, ts_recip),
 ccovar = NULL,
 itef1 = 30)
dinv <- solve(jac)
#estimate without the use of RSiena
ts_estim(net1 = s501,
net2 = s502,
statistics = list(ts_degree, ts_recip),
nite = 30,
 phase1 = FALSE)
 #estimate without the use of RSiena
ts_estim(net1 = s501,
net2 = s502,
statistics = list(ts_degree, ts_recip),
nite = 30,
itef1 = 10,
phase1 = TRUE)
#estimate without the use of RSiena
ts_estim(net1 = s501,
 net2 = s502,
 statistics = list(ts_degree, ts_recip),
 nite = 30,
 itef1 = 10,
 phase1 = TRUE,
 itef3 = 10,
 phase3 = TRUE)
# Phase 3 only
startvalues <- c(5.5, -2.2, 2.4)
stat <- list(ts_degree, ts_recip)
ts_phase3(startvalues = startvalues,
net1 = s501,
statistics = stat,
itef3 = 10,
verbose = TRUE)
library(RSiena)
mynet <- sienaDependent(array(c(s501, s502), dim=c(50, 50, 2)))
mydata <- sienaDataCreate(mynet)
myalgorithm <- sienaAlgorithmCreate(cond=FALSE)
#toggle set conditional to retrieve the rate parameter in theta!
myeff <- getEffects(mydata)
ts_estim(mydata = mydata, myeff = myeff)
#warning, this may take a while!
ts_estim(mydata = mydata, myeff = myeff, phase3 = TRUE)
ans1 <- siena07(myalgorithm, data=mydata, effects=myeff)
ts_estim(ans1)
}