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#
# Copyright 2007-2019 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.
#------------------------------------------------------------------------------
# Author: Michael D. Hunter
# Date: 2014-12-03
# Filename: JointWLS.R
# Purpose: Test WLS on Joint ordinal-continuous data.
#------------------------------------------------------------------------------
#------------------------------------------------
# a useful function
rms <- function(x, y=NA){
if(is.matrix(x) && is.vector(y) && nrow(x) == length(y)){
sqrt(colMeans((x-y)^2))
} else if(is.matrix(x) && length(y) == 1 && is.na(y)){
apply(x, 2, FUN=rms, x=x)
} else{
sqrt(mean((x-y)^2))
}
}
#------------------------------------------------
# Load packages
# Generate data
require(mvtnorm)
require(Matrix)
require(OpenMx)
nvar <- 3
k <- .5
sigma <- matrix(k, nvar, nvar)
diag(sigma) <- 1
N <- 20000 #500 # 20000
set.seed(943)
cDat <- rmvnorm(N, sigma=sigma)
rawData <- (cDat>0) + (cDat>1)
rawData[rawData[,1]>1,1] <- 1
cCor <- cor(cDat)
oCor <- cor(rawData)
rawData <- data.frame(
mxFactor(as.data.frame(rawData[,1]), 0:1),
mxFactor(as.data.frame(rawData[,2:nvar]), 0:2)
)
names(rawData) <- letters[(27-nvar):26]
nam <- names(rawData)
#------------------------------------------------
# Create joint data
# Create WLS data
# Fit Joint ML model
# Fit various least squares models
jdat <- data.frame(rawData, scale(cDat+rnorm(prod(dim(cDat)))))
names(jdat) <- c(nam, paste(nam, 'Con', sep=''))
jam <- names(jdat)
nvar <- ncol(jdat)
nord <- 3
nFactors <- 1
nThresholds <- 2
jod <- mxModel("jointThresholdModel",
mxMatrix("Full", nvar, nFactors, values=0.2, free=TRUE, lbound=-.99, ubound=.99, name="L"),
mxMatrix("Unit", nvar, 1, name="vectorofOnes"),
mxMatrix("Zero", 1, nvar, name="M"),
mxAlgebra(vectorofOnes - (diag2vec(L %*% t(L))) , name="E"),
mxAlgebra(L %*% t(L) + vec2diag(E), name="impliedCovs"),
mxMatrix("Full", nrow=nThresholds, ncol=nord, values=c(.2, NA, rep(c(.2, .4), 2)), free=c(TRUE, FALSE, rep(TRUE, 4)), name="thresholdMatrix", dimnames = list(c(), nam)),
mxFitFunctionML(),
mxExpectationNormal(covariance="impliedCovs", means="M", dimnames = jam, thresholds="thresholdMatrix", threshnames=nam),
mxData(observed=jdat, type='raw'))
#ML
jodr <- mxRun(jod)
# WLS
#jow <- mxModel(jod, name="jointThesholdModelWls", r, mxFitFunctionWLS(),
# mxExpectationNormal(covariance="impliedCovs", dimnames = jam, thresholds="thresholdMatrix", threshnames=nam))
jow <- mxModel(jod, name="jointThesholdModelWls", mxFitFunctionWLS())
jowr <- mxRun(jow)
# DWLS
jodw <- mxModel(jow, name="jointThesholdModelDwls", mxFitFunctionWLS('DWLS'))
jodwr <- mxRun(jodw)
#ULS
jou <- mxModel(jow, name="jointThesholdModelUls", mxFitFunctionWLS('ULS'))
jour <- mxRun(jou)
round(sres <- cbind(ML=omxGetParameters(jodr), WLS=omxGetParameters(jowr), DWLS=omxGetParameters(jodwr), ULS=omxGetParameters(jour)), 4)
rms(sres)
# non full WLS estimates are very close to ML
omxCheckTrue(all(rms(sres)[-2,-2] < 0.02))
# full WLS estimates are off due to model misspecification
omxCheckTrue(all(rms(sres)[,2] < 0.15))
#------------------------------------------------------------------------------
# alternative joint model
# Check the standardization for Joint
jodm <- mxModel("jointThresholdModel",
mxMatrix("Full", nvar, nFactors, values=0.2, free=TRUE, lbound=-.99, ubound=.99, name="L"),
mxMatrix("Unit", nvar, 1, name="vectorofOnes"),
mxMatrix("Full", 1, nvar, name="M", free=TRUE),
mxAlgebra(vectorofOnes - (diag2vec(L %*% t(L))) , name="E"),
mxAlgebra(L %*% t(L) + vec2diag(E), name="impliedCovs"),
mxMatrix("Full", nThresholds, nord, values=c(-1, NA, -1, 0, -2, -1), name="thresholdMatrix", free=FALSE, dimnames = list(c(), nam)),
mxFitFunctionML(),
mxExpectationNormal(covariance="impliedCovs", means="M", dimnames = jam, thresholds="thresholdMatrix", threshnames=nam),
mxData(observed=jdat, type='raw'))
jodmr <- mxRun(jodm)
jowm <- mxModel(jodm, name="jointThesholdModelWls", mxFitFunctionWLS())
jowmr <- mxRun(jowm)
# DWLS
jodwm <- mxModel(jowm, name="jointThesholdModelDwls", mxFitFunctionWLS('DWLS'))
jodwmr <- mxRun(jodwm)
#ULS
joum <- mxModel(jowm, name="jointThesholdModelUls", mxFitFunctionWLS('ULS'))
joumr <- mxRun(joum)
round( stres <- cbind(ML=coef(jodmr), WLS=coef(jowmr), DWLS=coef(jodwmr), ULS=coef(joumr)), 4)
# Note that when the fixed thresholds are set to have a distance much GREATER or
# much LESS than 1.0, I believe this contradicts the Total Variance of 1
# "constraint" in mxAlgebra "E". This makes the WLS/DWLS/ULS estimator diverge
# from the ML.
rms(stres)
# non full WLS estimates are very close to ML
omxCheckTrue(all(rms(stres)[-2,-2] < 0.02))
# full WLS estimates are off due to model misspecification
omxCheckTrue(all(rms(stres)[,2] < 0.15))
#------------------------------------------------------------------------------
# End
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