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#
# Copyright 2007-2018 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(nlme)
# Multilevel Long Format Test
# Author: Steve Boker
# Date: Sun Nov 29 14:06:07 EST 2009
# This script is used to test the multilevel long format
# functionality using definition variables as indices.
totalOccasions <- 100
totalSubjects <- 10L
set.seed(42) # repeatibility
tID <- rep(1:totalSubjects, each=totalOccasions)
trueX <- rep(rnorm(totalOccasions, mean=0, sd=2), each=totalSubjects) +
rnorm(totalOccasions*totalSubjects, mean=0, sd=.2)
trueB <- rep(rnorm(totalSubjects, mean=.8, sd=.3), each=totalOccasions)
tDataFrame <- data.frame(
ID=tID, X=trueX, Y=trueB*trueX +
rnorm(totalOccasions*totalSubjects,mean=0, sd=.1),trueB=trueB)
summary(tDataFrame)
manifestVars <- c("X", "Y")
numSubjects <- length(unique(tDataFrame$ID))
# Estimates the sum of the random and fixed effects
multilevelModel2 <- mxModel("Multilevel_2",
mxMatrix("Full", nrow=numSubjects, ncol=2,
values=c(.2,0),
free=c(TRUE, TRUE),
name="Rand",
byrow=TRUE
),
mxMatrix("Full", 2, 2,
labels=c(NA, NA,
"randrow[1,1]", NA),
free=FALSE,
name="A",
byrow=TRUE
),
mxMatrix("Symm", 2, 2,
values=c(.9,0,.9),
free=c(T,
F, T),
labels=c("varX",
NA, "varY"),
name="S",
byrow=TRUE
),
mxMatrix("Full", 2, 2,
values=c(1,0,
0,1),
free=FALSE,
byrow=TRUE, name="F"),
mxMatrix("Iden", 2, name="I"),
mxAlgebra(F %*% solve(I-A) %*% S %*% t(solve(I-A)) %*% t(F),
name="R",
dimnames = list(manifestVars, manifestVars)
),
mxMatrix("Full", nrow=1, ncol=length(manifestVars),
values=0,
free=FALSE,
labels=c(NA,"randrow[1,2]"),
dimnames=list(NULL, manifestVars),
name="M"
),
mxAlgebra(Rand[data.ID,], name="randrow"),
mxFitFunctionML(),mxExpectationNormal(covariance="R", means="M"),
mxData(tDataFrame, type="raw")
)
# ----------------------------------
# Fit the model and examine the summary results.
multilevelModel2Fit <- mxRun(multilevelModel2)
summary(multilevelModel2Fit)
lmeOut <- lme(Y~X, random= ~ X | ID, data=tDataFrame)
cbind(multilevelModel2Fit$output$estimate[1:numSubjects],
lmeOut$coef$random$ID[,2] + lmeOut$coef$fixed[2],
trueB[seq(1,totalOccasions*(totalSubjects), by=totalOccasions)])
mean(multilevelModel2Fit$output$estimate[1:numSubjects])
est <- multilevelModel2Fit$output$estimate
omxCheckCloseEnough(mean(est[1:numSubjects]),
lmeOut$coef$fixed[2], 0.001)
omxCheckCloseEnough(mean(est[(1:numSubjects) + (1*numSubjects)]),
lmeOut$coef$fixed[1], 0.001)
# ----------------------------------
# An OpenMx equivalent to the mixed model
perID <- mxModel(
"perID", type="RAM", latentVars=c('int', 'slope'),
mxData(data.frame(ID=1L:totalSubjects), "raw", primaryKey="ID"),
mxPath(c('int', 'slope'),c('int', 'slope'),'unique.pairs',
arrows=2,values=c(1,0,1)))
occa <- mxModel(
"occa", type="RAM", perID, manifestVars="Y", latentVars="lX",
mxData(tDataFrame, 'raw'),
mxPath('Y', arrows=2, values=1),
mxPath('one', 'Y'),
mxPath('one', 'lX', labels='data.X', free=FALSE),
mxPath('lX', 'Y'),
mxPath('perID.int', 'Y', values=1, free=FALSE, joinKey='ID'),
mxPath('perID.slope', 'Y', labels='data.X', free=FALSE, joinKey='ID'))
if (0) {
require(lme4)
lmer1 <- lmer(Y~X + (X | ID), data=tDataFrame, REML=FALSE)
pt1 <- occa
#pt1$perID$cholS$values[,] <- chol(VarCorr(lmer1)$ID)
pt1$perID$S$values[,] <- VarCorr(lmer1)$ID
pt1$A$values['Y', 'lX'] <- fixef(lmer1)['X']
pt1$M$values[,'Y'] <- fixef(lmer1)['(Intercept)']
pt1$S$values['Y', 'Y'] <- getME(lmer1, "sigma")^2
pt1 <- mxRun(mxModel(pt1, mxComputeSequence(list(
mxComputeOnce('fitfunction', 'fit'),
mxComputeReportExpectation()))))
omxCheckCloseEnough(logLik(pt1), logLik(lmer1), 1e-6)
}
occa <- mxRun(occa)
# a tad better than lme, same as lmer
omxCheckCloseEnough(occa$output$fit, -1725.954, 1e-2)
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