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# ---------------------------------------------------------------------
# Program: RAM-3Factor-12Indicators.R
# Author: Steven M. Boker
# Date: Fri Jul 30 13:45:12 EDT 2010
#
# This program is a factor model using standard RAM.
#
# ---------------------------------------------------------------------
# Revision History
# -- Fri Jul 30 13:45:12 EDT 2010
# Created RAM-3Factor-12Indicators.R.
#
# ---------------------------------------------------------------------
# ----------------------------------
# Read libraries and set options.
library(OpenMx)
options(width=100)
set.seed(10)
# ---------------------------------------------------------------------
# Data for factor model.
numberSubjects <- 1000
numberFactors <- 3
numberIndPerFactor <- 40
numberIndicators <- numberIndPerFactor*numberFactors # must be a multiple of numberFactors
XMatrix <- matrix(rnorm(numberSubjects*numberFactors, mean=0, sd=1), numberSubjects, numberFactors)
tLoadings <- c(1, seq(.5, .9, length.out=(numberIndPerFactor-1)), rep(0, numberIndPerFactor*2),
rep(0, numberIndPerFactor*1), 1, seq(.5, .9, length.out=(numberIndPerFactor-1)), rep(0, numberIndPerFactor*1),
rep(0, numberIndPerFactor*2), 1, seq(.5, .9, length.out=(numberIndPerFactor-1)))
BMatrix <- matrix(tLoadings, numberFactors, numberIndicators, byrow=TRUE)
UMatrix <- matrix(rnorm(numberSubjects*numberIndicators, mean=0, sd=1), numberSubjects, numberIndicators)
YMatrix <- XMatrix %*% BMatrix + UMatrix
cor(XMatrix)
dimnames(YMatrix) <- list(NULL, paste("X", 1:numberIndicators, sep=""))
YFrame <- data.frame(YMatrix)
round(cor(YFrame), 3)
round(cov(YFrame), 3)
indicators <- paste("X", 1:numberIndicators, sep="")
totalVars <- numberIndicators + numberFactors
# ----------------------------------
# Build an orthogonal simple structure factor model
latents <- paste("F", 1:numberFactors, sep="")
uniqueLabels <- paste("U_", indicators, sep="")
meanLabels <- paste("M_", latents, sep="")
factorVarLabels <- paste("Var_", latents, sep="")
latents1 <- latents[1]
indicators1 <- indicators[1:numberIndPerFactor]
loadingLabels1 <- paste("b_F1", indicators[1:numberIndPerFactor], sep="")
latents2 <- latents[2]
indicators2 <- indicators[numberIndPerFactor+(1:numberIndPerFactor)]
loadingLabels2 <- paste("b_F2", indicators[numberIndPerFactor+(1:numberIndPerFactor)], sep="")
latents3 <- latents[3]
indicators3 <- indicators[(2*numberIndPerFactor)+(1:numberIndPerFactor)]
loadingLabels3 <- paste("b_F3", indicators[(2*numberIndPerFactor)+(1:numberIndPerFactor)], sep="")
threeFactorOrthogonal <- mxModel("threeFactorOrthogonal",
type="RAM",
manifestVars=c(indicators),
latentVars=c(latents,"dummy1"),
mxPath(from=latents1, to=indicators1,
arrows=1, all=TRUE,
free=TRUE, values=.2,
labels=loadingLabels1),
mxPath(from=latents2, to=indicators2,
arrows=1, all=TRUE,
free=TRUE, values=.2,
labels=loadingLabels2),
mxPath(from=latents3, to=indicators3,
arrows=1, all=TRUE,
free=TRUE, values=.2,
labels=loadingLabels3),
mxPath(from=latents1, to=indicators1[1],
arrows=1,
free=FALSE, values=1),
mxPath(from=latents2, to=indicators2[1],
arrows=1,
free=FALSE, values=1),
mxPath(from=latents3, to=indicators3[1],
arrows=1,
free=FALSE, values=1),
mxPath(from=indicators,
arrows=2,
free=TRUE, values=.2,
labels=uniqueLabels),
mxPath(from=latents,
arrows=2,
free=TRUE, values=.8,
labels=factorVarLabels),
mxPath(from="one", to=indicators,
arrows=1, free=FALSE, values=0),
mxPath(from="one", to=c(latents),
arrows=1, free=TRUE, values=.1,
labels=meanLabels),
mxData(observed=cov(YFrame), means=mean(YFrame),
numObs=nrow(YFrame), type="cov")
)
threeFactorOrthogonalOut <- mxRun(threeFactorOrthogonal)
summary(threeFactorOrthogonalOut)
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