demo/OneFactorOrdinal01_MatrixRaw.R

In OpenMx/OpenMx: Extended Structural Equation Modelling

#
#   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
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# -----------------------------------------------------------------------
# Program: OneFactorOrdinal01_MatrixRaw.R  
# Author: Michael Neale
# Date: 2010.08.14 
#
# ModelType: Factor
# DataType: Ordinal
# Field: None
#
# Purpose: 
#      One Factor model to estimate factor loadings, residual variances and means
#      Matrix style model input - Raw data input - Ordinal data
#
# RevisionHistory:
#      Hermine Maes -- 2010.09.07 updated & reformatted & respecified
#      Ross Gore -- 2011.06.06	added Model, Data & Field metadata
#      Hermine Maes -- 2014.11.02 piecewise specification
# -----------------------------------------------------------------------------

require(OpenMx)
require(MASS)
# Load Libraries
# -----------------------------------------------------------------------------

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))

isIdentified(nVariables,nFactors) # if this function returns FALSE then model is not identified, otherwise it is.
# Set up simulation parameters: nVariables>=3, nThresholds>=1, nSubjects>=nVariables*nThresholds 
# and model should be identified
# -----------------------------------------------------------------------------


loadings     <- matrix(.7,nrow=nVariables,ncol=nFactors)
residuals    <- 1 - (loadings * loadings)
sigma        <- loadings %*% t(loadings) + vec2diag(residuals)
mu           <- matrix(0,nrow=nVariables,ncol=1)

set.seed(1234)
continuousData   <- mvtnorm::rmvnorm(n=nSubjects,mu,sigma)
# Simulate multivariate normal data
# -----------------------------------------------------------------------------

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))
}
# Chop continuous variables into ordinal data with nThresholds+1 
# approximately equal categories, based on 1st variable
# -----------------------------------------------------------------------------

ordinalData      <- mxFactor(as.data.frame(ordinalData),levels=c(1:(nThresholds+1)))
# Make the ordinal variables into R factors
# -----------------------------------------------------------------------------

fruitynames  <- paste("banana",1:nVariables,sep="")
names(ordinalData) <- fruitynames
# Name the variables
# -----------------------------------------------------------------------------

facLoads     <- mxMatrix( type="Full", nrow=nVariables, ncol=nFactors, 
                          free=TRUE, values=0.2, lbound=-.99, ubound=2, name="facLoadings" )
resVars      <- mxMatrix( type="Diag", nrow=nVariables, ncol=nVariables,
                          free=TRUE, values=0.9, name="resVariances" )
expCovs      <- mxAlgebra( expression=facLoadings %*% t(facLoadings) + resVariances, 
                          name="expCovariances" )
expMeans     <- mxMatrix( type="Zero", nrow=1, ncol=nVariables, name="expMeans" )
threDevs     <- mxMatrix( type="Full", nrow=nThresholds, ncol=nVariables,
                          free=rep( c(F,F,rep(T,(nThresholds-2))), nVariables), 
                          values=rep( c(0,1,rep(.2,(nThresholds-2))), nVariables),
                          lbound=rep( c(-Inf,rep(.01,(nThresholds-1))), nVariables),
                          dimnames=list(c(), fruitynames), name="thresholdDeviations" )
unitLower    <- mxMatrix( type="Lower", nrow=nThresholds, ncol=nThresholds,
                          free=FALSE, values=1, name="unitLower" )
expThres     <- mxAlgebra( expression=unitLower %*% thresholdDeviations, 
                          name="expThresholds" )
colOnes      <- mxMatrix( type="Unit", nrow=nThresholds, ncol=1, name="columnofOnes" )
matMeans     <- mxAlgebra( expression=expMeans %x% columnofOnes, name="meansMatrix" )
matVars      <- mxAlgebra( expression=sqrt(t(diag2vec(expCovariances))) %x% columnofOnes,
                           name="variancesMatrix" )
matThres     <- mxAlgebra( expression=(expThresholds - meansMatrix) / variancesMatrix,
                           name="thresholdMatrix" )
identity     <- mxMatrix( type="Iden", nrow=nVariables, ncol=nVariables, name="Identity" )
stFacLoads   <- mxAlgebra( expression=solve(sqrt(Identity * expCovariances)) %*% facLoadings,
                           name="standFacLoadings" )
dataRaw      <- mxData( observed=ordinalData, type='raw' )
exp          <- mxExpectationNormal( covariance="expCovariances", means="expMeans", 
                                     dimnames=fruitynames, thresholds="expThresholds" )
funML        <- mxFitFunctionML()

oneFactorThreshold01Model <- mxModel("oneFactorThreshold01Model", dataRaw,
                                   facLoads, resVars, expCovs, expMeans, threDevs, 
                                   unitLower, expThres, 
                                   colOnes, matMeans, matVars, matThres, identity,
                                   stFacLoads, dataRaw, exp, funML )

# Create Factor Model with Raw Ordinal Data and Matrices Input
# -----------------------------------------------------------------------------

oneFactorThreshold01Fit <- mxRun(oneFactorThreshold01Model, suppressWarnings=TRUE)
# Fit the model with mxRun
# -----------------------------------------------------------------------------

summary(oneFactorThreshold01Fit)
# Print a summary of the results
# -----------------------------------------------------------------------------