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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.
# -----------------------------------------------------------------------
# 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
# -----------------------------------------------------------------------------
require(OpenMx)
# 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
# -------------------------------------
# Simulate Data
# -----------------------------------------------------------------------------
oneFactorThresholdModel01 <- mxModel("oneFactorThresholdModel01",
mxMatrix(
type="Full",
nrow=nVariables,
ncol=nFactors,
free=TRUE,
values=0.2,
lbound=-.99,
ubound=2,
name="facLoadings"
),
mxMatrix(
type="Diag",
nrow=nVariables,
ncol=nVariables,
free=TRUE,
values=0.9,
name="resVariances"
),
mxAlgebra(
expression=facLoadings %*% t(facLoadings) + resVariances,
name="expCovariances"
),
mxMatrix(
type="Full",
nrow=1,
ncol=nVariables,
free=T,
name="expMeans"
),
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"
),
mxMatrix(
type="Lower",
nrow=nThresholds,
ncol=nThresholds,
free=FALSE,
values=1,
name="unitLower"
),
mxAlgebra(
expression=unitLower %*% thresholdDeviations,
name="expThresholds"
),
mxMatrix(
type="Unit",
nrow=nThresholds,
ncol=1,
name="columnofOnes"
),
mxAlgebra(
expression=expMeans %x% columnofOnes,
name="meansMatrix"
),
mxAlgebra(
expression=sqrt(t(diag2vec(expCovariances))) %x% columnofOnes,
name="variancesMatrix"
),
mxAlgebra(
expression=(expThresholds - meansMatrix) / variancesMatrix,
name="thresholdMatrix"
),
mxMatrix(
type="Iden",
nrow=nVariables,
ncol=nVariables,
name="Identity"
),
mxAlgebra(
expression=solve(sqrt(Identity * expCovariances)) %*% facLoadings,
name="facLoadingsMatrix"
),
mxData(
observed=ordinalData,
type='raw'
),
mxFitFunctionML(),mxExpectationNormal(
covariance="expCovariances",
means="expMeans",
dimnames=fruitynames,
thresholds="expThresholds"
)
)
# Create Factor Model with Raw Ordinal Data and Matrices Input
# -----------------------------------------------------------------------------
oneFactorThresholdFit01 <- mxTryHard(oneFactorThresholdModel01)
# Fit the model with mxRun
# -----------------------------------------------------------------------------
summary(oneFactorThresholdFit01)
# Print a summary of the results
# -----------------------------------------------------------------------------
omxCheckCloseEnough(oneFactorThresholdFit01$output$fit, 6281.99, .1)
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