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#
# Copyright 2007-2019 by the individuals mentioned in the source code history
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# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
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# OpenMx Ordinal Data Example
# Revision history:
# Michael Neale 14 Aug 2010
#
# Step 1: load libraries
require(OpenMx)
if (mxOption(NULL, "Default optimizer") == 'NPSOL') stop('SKIP')
#
# Step 2: set up simulation parameters
# Note: nVariables>=3, nThresholds>=1, nSubjects>=nVariables*nThresholds (maybe more)
# and model should be identified
#
nVariables<-5
nFactors<-1
nThresholds<-3
nSubjects<-500
isIdentified<-function(nVariables,nFactors) as.logical(1+sign((nVariables*(nVariables-1)/2) - nVariables*nFactors + nFactors*(nFactors-1)/2))
# if this function returns FALSE then model is not identified, otherwise it is.
isIdentified(nVariables,nFactors)
loadings <- matrix(.7,nrow=nVariables,ncol=nFactors)
residuals <- 1 - (loadings * loadings)
sigma <- loadings %*% t(loadings) + vec2diag(residuals)
mu <- matrix(0,nrow=nVariables,ncol=1)
# Step 3: simulate multivariate normal data
set.seed(1234)
continuousData <- mvtnorm::rmvnorm(n=nSubjects,mu,sigma)
# Step 4: chop continuous variables into ordinal data
# with nThresholds+1 approximately equal categories, based on 1st variable
quants<-quantile(continuousData[,1], probs = c((1:nThresholds)/(nThresholds+1)))
ordinalData<-matrix(0,nrow=nSubjects,ncol=nVariables)
for(i in 1:nVariables)
{
ordinalData[,i] <- cut(as.vector(continuousData[,i]),c(-Inf,quants,Inf))
}
# Step 5: make the ordinal variables into R factors
ordinalData <- mxFactor(as.data.frame(ordinalData),levels=c(1:(nThresholds+1)))
# Step 6: name the variables
fruitynames<-paste("banana",1:nVariables,sep="")
names(ordinalData)<-fruitynames
thresholdModel <- mxModel("thresholdModel",
mxMatrix("Full", nVariables, nFactors, values=0.2, free=TRUE, lbound=-.99, ubound=.99, name="L"),
mxMatrix("Unit", nVariables, 1, name="vectorofOnes"),
mxMatrix("Zero", 1, nVariables, name="M"),
mxAlgebra(vectorofOnes - (diag2vec(L %*% t(L))) , name="E"),
mxAlgebra(L %*% t(L) + vec2diag(E), name="impliedCovs"),
mxMatrix("Full",
name="thresholdDeviations", nrow=nThresholds, ncol=nVariables,
values=.2,
free = TRUE,
lbound = rep( c(-Inf,rep(.01,(nThresholds-1))) , nVariables),
dimnames = list(c(), fruitynames)),
mxMatrix("Lower",nThresholds,nThresholds,values=1,free=F,name="unitLower"),
mxAlgebra(unitLower %*% thresholdDeviations, name="thresholdMatrix"),
mxFitFunctionML(),mxExpectationNormal(covariance="impliedCovs", means="M", dimnames = fruitynames, thresholds="thresholdMatrix"),
mxData(observed=ordinalData, type='raw')
)
thresholdModelrun <- mxRun(thresholdModel)
thresholdSaturated <- mxRefModels(thresholdModelrun, run=TRUE)
summary(thresholdModelrun, refModels=thresholdSaturated)
a <- Sys.time()
thresholdModelAuto <- mxAutoStart(thresholdModel)
b <- Sys.time()
b-a # about 2 seconds on my laptop (as of 2.12.2.169 [GIT v2.12.2-169-gb745620], this is ~ .07 seconds on 3.3 GHz Intel Core i7 iMac)
thresholdModelAutoRun <- mxRun(thresholdModelAuto)
(b-a) + summary(thresholdModelAutoRun)$wallTime
summary(thresholdModelrun)$wallTime
# 37 sec for the automatic start values time plus the estimation time from the auto starts
# 64 sec for the estimation time from the user starts
# auto starts provides a net boost in performance
# As of 2.12.2.169 [GIT v2.12.2-169-gb745620], this is auto+ = 13.62 Secs vs 10.38 Secs for user starts (on 3.3 GHz Intel Core i7 iMac)
a <- proc.time()
thresholdModelWLS <- mxModel(thresholdModel, name="WLSThresholdModel",
mxData(ordinalData, 'raw'),
mxMatrix('Zero', nrow=1, ncol=nVariables, name='impliedMeans'),
mxExpectationNormal(covariance="impliedCovs", means='impliedMeans', dimnames = fruitynames, thresholds="thresholdMatrix"),
mxFitFunctionWLS('ULS'))
thresholdModelWLSrun <- mxRun(thresholdModelWLS)
b <- proc.time()
b-a # 0.065 Secs 2.12.2.169 [GIT v2.12.2-169-gb745620] on 3.3 GHz Intel Core i7 iMac)
summary(thresholdModelWLSrun)$wallTime # .035 Secs
wls.L <- mxEval(L, thresholdModelWLSrun) #should be all 0.7
wls.T <- mxEval(thresholdMatrix, thresholdModelWLSrun) #should be all quants
ml.L <- mxEval(L, thresholdModelrun) #should be all 0.7
ml.T <- mxEval(thresholdMatrix, thresholdModelrun) #should be all quants
auto.L <- mxEval(L, thresholdModelAuto)
auto.T <- mxEval(thresholdMatrix, thresholdModelAuto, compute=TRUE)
rms <- function(x, y){sqrt(mean((x-y)^2))}
omxCheckTrue(rms(wls.L, .7) < 0.025)
rms(ml.L, .7)
omxCheckTrue(rms(ml.L, auto.L) < 0.01)
omxCheckTrue(rms(wls.T, quants) < 0.05)
rms(ml.T, quants)
print(rms(wls.L, auto.L))
omxCheckTrue(rms(wls.L, auto.L) < 1e-6)
print(rms(wls.T, auto.T))
omxCheckTrue(rms(wls.T, auto.T) < 2e-5)
ml.sum <- summary(thresholdModelrun, refModels=thresholdSaturated)
wls.sum <- summary(thresholdModelWLSrun)
omxCheckWithinPercentError(wls.sum$Chi, 0.653, percent=10)
omxCheckWithinPercentError(ml.sum$Chi, wls.sum$Chi, percent=16)
omxCheckEquals(ml.sum$ChiDoF, wls.sum$ChiDoF)
ciModel <- mxModel(thresholdModelWLSrun, mxCI("L"))
omxCheckError(mxRun(ciModel, intervals=TRUE), "Confidence intervals are not supported for DWLS or ULS. Try mxSE or switch 'WLSThresholdModel' to full WLS")
#------------------------------------------------------------------------------
tmod2 <- mxModel("thresholdModel2",
mxMatrix("Full", nVariables, nFactors, values=0.2, free=TRUE, lbound=-.99, ubound=1.5, name="L"),
mxMatrix("Diag", nVariables, nVariables, values=.1, free=TRUE, lbound=1e-8, name="R"),
mxMatrix("Unit", nVariables, 1, name="vectorofOnes"),
mxMatrix("Full", 1, nVariables, values=0, free=TRUE, name="M"),
mxAlgebra(L %*% t(L) + R, name="impliedCovs"),
mxMatrix("Full", nThresholds, nVariables, values=c(0, 1, 2), name="Thresh"),
mxFitFunctionML(),
mxExpectationNormal(covariance="impliedCovs", means="M", dimnames = fruitynames, thresholds="Thresh"),
mxData(observed=ordinalData, type='raw')
)
trun2 <- mxRun(tmod2)
a <- proc.time()
wmod2 <- mxModel(tmod2, mxData(ordinalData, 'raw'),
mxFitFunctionWLS(),
mxAlgebra(cov2cor(impliedCovs), name='newCov'),
mxMatrix("Unit", nrow=nThresholds, ncol=1, name="UnitVector"),
mxAlgebra(UnitVector %x% t(sqrt(diag2vec(impliedCovs))), name='theStandardDeviations'),
mxAlgebra(UnitVector %x% M, name='theM'),
mxAlgebra( (Thresh-theM)/theStandardDeviations, name='newThresh'),
mxMatrix('Zero', 1, nVariables, name='MZ'),
mxExpectationNormal(covariance='newCov', means='MZ', thresholds='newThresh', dimnames = fruitynames) #N.B. means left out on purpose
)
#mxEval(theM, wmod2, compute=TRUE)
#mxEval(Thresh, wmod2, compute=TRUE)
#mxEval(theStandardDeviations, wmod2, compute=TRUE)
#mxEval(newCov, wmod2, compute=TRUE)
#mxEval(newThresh, wmod2, compute=TRUE)
wrun2 <- mxRun(wmod2)
b <- proc.time()
b-a
summary(trun2)$wallTime
cbind(omxGetParameters(trun2), omxGetParameters(wrun2))
plot(omxGetParameters(trun2), omxGetParameters(wrun2))
abline(a=0, b=1)
omxCheckCloseEnough(rms(omxGetParameters(trun2), omxGetParameters(wrun2)), 0, .035)
omxCheckCloseEnough(cor(omxGetParameters(trun2), omxGetParameters(wrun2)), 1, .06)
# new style for model 2
wmod2a <- mxModel(tmod2, mxData(ordinalData, 'raw'), mxFitFunctionWLS())
wrun2a <- mxRun(wmod2a)
cbind(omxGetParameters(trun2), omxGetParameters(wrun2), omxGetParameters(wrun2a))
# Check that old/hard stadardization and new/easy standardization give the same
# answer.
omxCheckCloseEnough(omxGetParameters(wrun2), omxGetParameters(wrun2a), 1e-4)
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