# ---------------------------------------------------------------------
# Program: TwoFactorOrthoCov-OpenMx100221.R
#  Author: Steven M. Boker
#    Date: Sun Feb 21 14:00:09 EST 2010
#
# This program fits a covariance single factor model to the 
#     factorExample1.csv simulated data.
#
#
# ---------------------------------------------------------------------
# Revision History
#    -- Sun Feb 21 14:00:12 EST 2010
#      Created TwoFactorOrthoCov-OpenMx100221.R.
#
# ---------------------------------------------------------------------

# ----------------------------------
# Read libraries and set options.

options(width=80)

require(psych)
require(OpenMx)

# ----------------------------------
# Read the data and print descriptive statistics.

factorExample1 <- read.csv("factorExample1.csv")

describe(factorExample1)

# ----------------------------------
# Build an OpenMx two factor orthogonal covariance model with fixed variance

indicators <- names(factorExample1)
latents <- c("F1", "F2")
loadingLabels <- c(paste("b_F1", indicators, sep=""), paste("b_F2", indicators, sep=""))
uniqueLabels <- paste("U_", indicators, sep="")
meanLabels <- paste("M_", indicators, sep="")
factorVarLabels <- paste("Var_", latents, sep="")

twoFactorOrthoCov1 <- mxModel("Two Factor Orthogonal Covariance Model with Fixed Variance",
    type="RAM",
    manifestVars=indicators,
    latentVars=latents,
    mxPath(from=latents, to=indicators, 
           arrows=1, all=TRUE, 
           free=TRUE, values=.2, 
           labels=loadingLabels),
    mxPath(from=indicators, 
           arrows=2, 
           free=TRUE, values=.8, 
           labels=uniqueLabels),
    mxPath(from=latents,
           arrows=2, 
           free=FALSE, values=1, 
           labels=factorVarLabels),
    mxData(observed=cov(factorExample1), type="cov", numObs=500)
    )

twoFactorOrthoCov1Out <- mxRun(twoFactorOrthoCov1)

summary(twoFactorOrthoCov1Out)


# ----------------------------------
# Build an OpenMx two factor orthogonal covariance model with fixed loading


twoFactorOrthoCov2 <- mxModel("Two Factor Orthogonal Covariance Model with Fixed Loading",
    type="RAM",
    manifestVars=indicators,
    latentVars=latents,
    mxPath(from=latents, to=indicators, 
           arrows=1, all=TRUE,
           free=TRUE, values=.2, 
           labels=loadingLabels),
    mxPath(from=indicators, 
           arrows=2, 
           free=TRUE, values=.8, 
           labels=uniqueLabels),
    mxPath(from=latents,
           arrows=2,
           free=TRUE, values=1, 
           labels=factorVarLabels),
    mxPath(from=latents, to=c("x1", "x1"),
           arrows=1, 
           free=FALSE, values=1),
    mxData(observed=cov(factorExample1), type="cov", numObs=500)
    )

twoFactorOrthoCov2Out <- mxRun(twoFactorOrthoCov2)

summary(twoFactorOrthoCov2Out)