#
# Copyright 2007-2019 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: TwoFactorModel_PathCov.R
# Author: Ryne Estabrook
# Date: 2009.08.01
#
# ModelType: Factor
# DataType: Continuous
# Field: None
#
# Purpose:
# Two Factor model to estimate factor loadings, residual variances and means
# Path style model input - Covariance matrix data input
#
# RevisionHistory:
# Hermine Maes -- 2009.10.08 updated & reformatted
# Ross Gore -- 2011.06.06 added Model, Data & Field metadata
# Hermine Maes -- 2014.11.02 piecewise specification
# -----------------------------------------------------------------------------
require(OpenMx)
# Load Library
# -----------------------------------------------------------------------------
myFADataCov <- matrix(
c(0.997, 0.642, 0.611, 0.672, 0.637, 0.677, 0.342, 0.299, 0.337,
0.642, 1.025, 0.608, 0.668, 0.643, 0.676, 0.273, 0.282, 0.287,
0.611, 0.608, 0.984, 0.633, 0.657, 0.626, 0.286, 0.287, 0.264,
0.672, 0.668, 0.633, 1.003, 0.676, 0.665, 0.330, 0.290, 0.274,
0.637, 0.643, 0.657, 0.676, 1.028, 0.654, 0.328, 0.317, 0.331,
0.677, 0.676, 0.626, 0.665, 0.654, 1.020, 0.323, 0.341, 0.349,
0.342, 0.273, 0.286, 0.330, 0.328, 0.323, 0.993, 0.472, 0.467,
0.299, 0.282, 0.287, 0.290, 0.317, 0.341, 0.472, 0.978, 0.507,
0.337, 0.287, 0.264, 0.274, 0.331, 0.349, 0.467, 0.507, 1.059),
nrow=9,
dimnames=list(
c("x1", "x2", "x3", "x4", "x5", "x6", "y1", "y2", "y3"),
c("x1", "x2", "x3", "x4", "x5", "x6", "y1", "y2", "y3")),
)
twoFactorCov <- myFADataCov[c("x1","x2","x3","y1","y2","y3"),c("x1","x2","x3","y1","y2","y3")]
myFADataMeans <- c(2.988, 3.011, 2.986, 3.053, 3.016, 3.010, 2.955, 2.956, 2.967)
names(myFADataMeans) <- c("x1", "x2", "x3", "x4", "x5", "x6", "y1", "y2", "y3")
twoFactorMeans <- myFADataMeans[c(1:3,7:9)]
# Prepare Data
# -----------------------------------------------------------------------------
dataCov <- mxData( observed=twoFactorCov, type="cov", numObs=500, means=twoFactorMeans )
# residual variances
resVars <- mxPath( from=c("x1", "x2", "x3", "y1", "y2", "y3"), arrows=2,
free=TRUE, values=c(1,1,1,1,1,1),
labels=c("e1","e2","e3","e4","e5","e6") )
# latent variances and covariance
latVars <- mxPath( from=c("F1","F2"), arrows=2, connect="unique.pairs",
free=TRUE, values=c(1,.5,1), labels=c("varF1","cov","varF2") )
# factor loadings for x variables
facLoadsX <- mxPath( from="F1", to=c("x1","x2","x3"), arrows=1,
free=c(F,T,T), values=c(1,1,1), labels=c("l1","l2","l3") )
# factor loadings for y variables
facLoadsY <- mxPath( from="F2", to=c("y1","y2","y3"), arrows=1,
free=c(F,T,T), values=c(1,1,1), labels=c("l4","l5","l6") )
# means
means <- mxPath( from="one", to=c("x1","x2","x3","y1","y2","y3","F1","F2"),
arrows=1,
free=c(T,T,T,T,T,T,F,F), values=c(1,1,1,1,1,1,0,0),
labels=c("meanx1","meanx2","meanx3",
"meany1","meany2","meany3",NA,NA) )
twoFactorModel <- mxModel("Two Factor Model Path Specification", type="RAM",
manifestVars=c("x1", "x2", "x3", "y1", "y2", "y3"),
latentVars=c("F1","F2"),
dataCov, resVars, latVars, facLoadsX, facLoadsY, means)
# Create an MxModel object
# -----------------------------------------------------------------------------
twoFactorFit <- mxRun(twoFactorModel)
summary(twoFactorFit)
coef(twoFactorFit)
omxCheckCloseEnough(coef(twoFactorFit)[["l2"]], 0.9720, 0.01)
omxCheckCloseEnough(coef(twoFactorFit)[["l3"]], 0.9310, 0.01)
omxCheckCloseEnough(coef(twoFactorFit)[["l5"]], 1.0498, 0.01)
omxCheckCloseEnough(coef(twoFactorFit)[["l6"]], 1.0533, 0.01)
omxCheckCloseEnough(coef(twoFactorFit)[["varF1"]], 0.6622, 0.01)
omxCheckCloseEnough(coef(twoFactorFit)[["varF2"]], 0.4510, 0.01)
omxCheckCloseEnough(coef(twoFactorFit)[["cov"]], 0.2958, 0.01)
omxCheckCloseEnough(coef(twoFactorFit)[["e1"]], 0.3348, 0.01)
omxCheckCloseEnough(coef(twoFactorFit)[["e2"]], 0.3994, 0.01)
omxCheckCloseEnough(coef(twoFactorFit)[["e3"]], 0.4101, 0.01)
omxCheckCloseEnough(coef(twoFactorFit)[["e4"]], 0.5420, 0.01)
omxCheckCloseEnough(coef(twoFactorFit)[["e5"]], 0.4809, 0.01)
omxCheckCloseEnough(coef(twoFactorFit)[["e6"]], 0.5586, 0.01)
omxCheckCloseEnough(coef(twoFactorFit)[["meanx1"]], 2.988, 0.01)
omxCheckCloseEnough(coef(twoFactorFit)[["meanx2"]], 3.011, 0.01)
omxCheckCloseEnough(coef(twoFactorFit)[["meanx3"]], 2.986, 0.01)
omxCheckCloseEnough(coef(twoFactorFit)[["meany1"]], 2.955, 0.01)
omxCheckCloseEnough(coef(twoFactorFit)[["meany2"]], 2.956, 0.01)
omxCheckCloseEnough(coef(twoFactorFit)[["meany3"]], 2.967, 0.01)
# Compare OpenMx results to Mx results
# -----------------------------------------------------------------------------
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