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#
# Copyright 2007-2020 by the individuals mentioned in the source code history
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
require(OpenMx)
require(snowfall)
sfInit(parallel = TRUE, cpus = imxGetNumThreads())
sfLibrary(OpenMx)
set.seed(10)
# parameters for the simulation: lambda = factor loadings,
# specifics = specific variances
lambda <- matrix(c(.8, .5, .7, 0), 4, 1)
nObs <- 500
nReps <- 1000
nVar <- nrow(lambda)
specifics <- diag(nVar)
chl <- chol(lambda %*% t(lambda) + specifics)
# indices for parameters and hessian estimate in results
pStrt <- 3
pEnd <- pStrt + 2*nVar - 1
hStrt <- pEnd + 1
hEnd <- hStrt + 2*nVar - 1
# dimension names for OpenMx
dn <- list()
dn[[1]] <- paste("Var", 1:4, sep="")
dn[[2]] <- dn[[1]]
# function to get a covariance matrix
randomCov <- function(nObs, nVar, chl, dn) {
x <- matrix(rnorm(nObs*nVar), nObs, nVar)
x <- x %*% chl
thisCov <- cov(x)
dimnames(thisCov) <- dn
return(thisCov)
}
createNewModel <- function(model, modelname) {
model$data$observed <- randomCov(nObs, nVar, chl, dn)
model <- mxModel(name=modelname, model)
return(model)
}
getStats <- function(model) {
retval <- c(code=model$output$status[[1]],
grad=sqrt(sum(model$output$gradient^2)),
model$output$estimate,
sqrt(2*diag(solve(model$output$hessian))))
return(retval)
}
# initialize obsCov for MxModel
obsCov <- randomCov(nObs, nVar, chl, dn)
# results matrix: get results for each simulation
results <- matrix(0, nReps, hEnd)
dnr <- c("inform", "normG", paste("lambda", 1:nVar, sep=""),
paste("specifics", 1:nVar, sep=""),
paste("hessLambda", 1:nVar, sep=""),
paste("hessSpecifics", 1:nVar, sep=""))
dimnames(results)[[2]] <- dnr
# instantiate MxModel
template <- mxModel(name="stErrSim",
mxMatrix(name="lambda", type="Full", nrow=4, ncol=1,
free=TRUE, values=c(.8, .5, .7, 0)),
mxMatrix(name="specifics", type="Diag", nrow=4,
free=TRUE, values=rep(1, 4)),
mxAlgebra(lambda %*% t(lambda) + specifics,
name="preCov", dimnames=dn),
mxData(observed=obsCov, type="cov", numObs=nObs),
mxExpectationNormal(covariance='preCov'),
mxFitFunctionML(),
independent = TRUE)
submodels <- lapply(1:nReps, function(x) {
createNewModel(template, paste('stErrSim', x, sep=''))
})
names(submodels) <- imxExtractNames(submodels)
topModel <- mxModel('container', submodels)
modelResults <- mxRun(topModel, silent=TRUE, suppressWarnings=TRUE)
results <- t(omxSapply(modelResults$submodels, getStats))
sfStop()
# get rid of bad covergence results
results2 <- results[which(results[,"code"] <= 1),]
# summarize the results
means <- colMeans(results2)
stdevs <- apply(results2, 2, sd)
sumResults <- data.frame(matrix(dnr[pStrt:pEnd], 2*nVar, 1,
dimnames=list(NULL, "Parameter")))
sumResults$mean <- means[pStrt:pEnd]
sumResults$obsStDev <- stdevs[pStrt:pEnd]
sumResults$meanHessEst <- means[hStrt:hEnd]
print(sumResults)
omxCheckCloseEnough(means["grad"], 0, .05)
omxCheckCloseEnough(sumResults$mean, c(lambda, diag(specifics)), .05)
omxCheckCloseEnough(sumResults$obsStDev, sumResults$meanHessEst, .05)
detach("package:snowfall")
unloadNamespace("snowfall")
detach("package:snow")
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