#
#   Copyright 2007-2017 The OpenMx Project
#
#   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: 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 <- 8
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=""))

round(cor(YMatrix), 3)
round(cov(YMatrix), 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, connect="all.pairs",
           free=TRUE, values=.2, ubound=5,
           labels=loadingLabels1),
    mxPath(from=latents2, to=indicators2, 
           arrows=1, connect="all.pairs",
           free=TRUE, values=.2, 
           labels=loadingLabels2),
    mxPath(from=latents3, to=indicators3, 
           arrows=1, connect="all.pairs",
           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, lbound=1e-6,
           labels=uniqueLabels),
    mxPath(from=latents,
           arrows=2, 
           free=TRUE, values=.8, lbound=1e-6,
           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(YMatrix), means=apply(YMatrix, 2, mean), 
	numObs=nrow(YMatrix), type="cov")
    )

threeFactorOrthogonalOut <- mxRun(threeFactorOrthogonal)
summary(threeFactorOrthogonalOut)
omxCheckCloseEnough(threeFactorOrthogonalOut$output$fit, 29350.18, .1)

# This is a starting point near a local minimum. Without the change in
# this commit, NPSOL will move to a worse point.
p1 <- c(66.8474253, 66.7162888, 86.988636, 79.99685, 105.6942539,  107.1596945, 119.0563245, 90.0791803, 97.111435, 116.3041677,  127.0225488, 138.8965557, 167.4370949, 161.1764251, 61.9541787,  73.1054388, 84.0847585, 89.8050077, 98.8327493, 114.9673433,  130.8809636, 2.0449374, 1.0203949, 1.0540143, 0.8909142, 1.0505263,  0.9483473, 0.9124185, 1.0120539, 2.1564055, 0.9999484, 0.9128441,  1.0096901, 1.0618295, 0.9599213, 1.0694914, 1.038408, 1.9846161,  1.0582464, 1.0689193, 1.0500171, 0.9396425, 1.0470683, 0.9089026,  1.0418309, 6.18e-05, 3.33e-05, 5.59e-05, 7.5e-06, -6.74e-05,  -7.11e-05)
threeFactorOrthogonal <- omxSetParameters(threeFactorOrthogonal, values=p1,
                                          labels = names(omxGetParameters(threeFactorOrthogonal)))
threeFactorOrthogonal$A$ubound <- NA
diag(threeFactorOrthogonal$A$lbound) <- 1e-6
threeFactorOrthogonalOut <- mxRun(threeFactorOrthogonal)
omxCheckCloseEnough(threeFactorOrthogonalOut$output$fit, 30855.58, .1)
