demo/TwoFactorModel_MatrixCov.R
In OpenMx/OpenMx: Extended Structural Equation Modelling
#
# 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_MatrixCov.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
# Matrix 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 -- 2014.11.04 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,
mean=twoFactorMeans )
dataRaw <- mxData( observed=myFADataRaw, type="raw" )
matrA <- mxMatrix( type="Full", nrow=8, ncol=8,
free= c(F,F,F,F,F,F,F,F,
F,F,F,F,F,F,T,F,
F,F,F,F,F,F,T,F,
F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,T,
F,F,F,F,F,F,F,T,
F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F),
values=c(0,0,0,0,0,0,1,0,
0,0,0,0,0,0,1,0,
0,0,0,0,0,0,1,0,
0,0,0,0,0,0,0,1,
0,0,0,0,0,0,0,1,
0,0,0,0,0,0,0,1,
0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0),
labels=c(NA,NA,NA,NA,NA,NA,"l1",NA,
NA,NA,NA,NA,NA,NA,"l2",NA,
NA,NA,NA,NA,NA,NA,"l3",NA,
NA,NA,NA,NA,NA,NA,NA,"l4",
NA,NA,NA,NA,NA,NA,NA,"l5",
NA,NA,NA,NA,NA,NA,NA,"l6",
NA,NA,NA,NA,NA,NA,NA,NA,
NA,NA,NA,NA,NA,NA,NA,NA),
byrow=TRUE, name="A" )
matrS <- mxMatrix( type="Symm", nrow=8, ncol=8,
free= c(T,F,F,F,F,F,F,F,
F,T,F,F,F,F,F,F,
F,F,T,F,F,F,F,F,
F,F,F,T,F,F,F,F,
F,F,F,F,T,F,F,F,
F,F,F,F,F,T,F,F,
F,F,F,F,F,F,T,T,
F,F,F,F,F,F,T,T),
values=c(1,0,0,0,0,0,0,0,
0,1,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,
0,0,0,1,0,0,0,0,
0,0,0,0,1,0,0,0,
0,0,0,0,0,1,0,0,
0,0,0,0,0,0,1,.5,
0,0,0,0,0,0,.5,1),
labels=c("e1",NA, NA, NA, NA, NA, NA, NA,
NA, "e2", NA, NA, NA, NA, NA, NA,
NA, NA, "e3", NA, NA, NA, NA, NA,
NA, NA, NA, "e4", NA, NA, NA, NA,
NA, NA, NA, NA, "e5", NA, NA, NA,
NA, NA, NA, NA, NA, "e6", NA, NA,
NA, NA, NA, NA, NA, NA,"varF1","cov",
NA, NA, NA, NA, NA, NA,"cov","varF2"),
byrow=TRUE, name="S" )
matrF <- mxMatrix( type="Full", nrow=6, ncol=8,
free=FALSE,
values=c(1,0,0,0,0,0,0,0,
0,1,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,
0,0,0,1,0,0,0,0,
0,0,0,0,1,0,0,0,
0,0,0,0,0,1,0,0),
byrow=TRUE, name="F" )
matrM <- mxMatrix( type="Full", nrow=1, ncol=8,
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",
"meanx4","meanx5","meanx6",NA,NA),
name="M" )
exp <- mxExpectationRAM("A","S","F","M",
dimnames=c("x1","x2","x3","y1","y2","y3","F1","F2"))
funML <- mxFitFunctionML()
twoFactorModel <- mxModel("Two Factor Model Matrix Specification",
dataCov, matrA, matrS, matrF, matrM, exp, funML)
# 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)[["meanx4"]], 2.955, 0.01)
omxCheckCloseEnough(coef(twoFactorFit)[["meanx5"]], 2.956, 0.01)
omxCheckCloseEnough(coef(twoFactorFit)[["meanx6"]], 2.967, 0.01)
# Compare OpenMx results to Mx results
# -----------------------------------------------------------------------------
OpenMx/OpenMx documentation built on April 17, 2024, 3:32 p.m.
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#
# 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_MatrixCov.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
# Matrix 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 -- 2014.11.04 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,
mean=twoFactorMeans )
dataRaw <- mxData( observed=myFADataRaw, type="raw" )
matrA <- mxMatrix( type="Full", nrow=8, ncol=8,
free= c(F,F,F,F,F,F,F,F,
F,F,F,F,F,F,T,F,
F,F,F,F,F,F,T,F,
F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,T,
F,F,F,F,F,F,F,T,
F,F,F,F,F,F,F,F,
F,F,F,F,F,F,F,F),
values=c(0,0,0,0,0,0,1,0,
0,0,0,0,0,0,1,0,
0,0,0,0,0,0,1,0,
0,0,0,0,0,0,0,1,
0,0,0,0,0,0,0,1,
0,0,0,0,0,0,0,1,
0,0,0,0,0,0,0,0,
0,0,0,0,0,0,0,0),
labels=c(NA,NA,NA,NA,NA,NA,"l1",NA,
NA,NA,NA,NA,NA,NA,"l2",NA,
NA,NA,NA,NA,NA,NA,"l3",NA,
NA,NA,NA,NA,NA,NA,NA,"l4",
NA,NA,NA,NA,NA,NA,NA,"l5",
NA,NA,NA,NA,NA,NA,NA,"l6",
NA,NA,NA,NA,NA,NA,NA,NA,
NA,NA,NA,NA,NA,NA,NA,NA),
byrow=TRUE, name="A" )
matrS <- mxMatrix( type="Symm", nrow=8, ncol=8,
free= c(T,F,F,F,F,F,F,F,
F,T,F,F,F,F,F,F,
F,F,T,F,F,F,F,F,
F,F,F,T,F,F,F,F,
F,F,F,F,T,F,F,F,
F,F,F,F,F,T,F,F,
F,F,F,F,F,F,T,T,
F,F,F,F,F,F,T,T),
values=c(1,0,0,0,0,0,0,0,
0,1,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,
0,0,0,1,0,0,0,0,
0,0,0,0,1,0,0,0,
0,0,0,0,0,1,0,0,
0,0,0,0,0,0,1,.5,
0,0,0,0,0,0,.5,1),
labels=c("e1",NA, NA, NA, NA, NA, NA, NA,
NA, "e2", NA, NA, NA, NA, NA, NA,
NA, NA, "e3", NA, NA, NA, NA, NA,
NA, NA, NA, "e4", NA, NA, NA, NA,
NA, NA, NA, NA, "e5", NA, NA, NA,
NA, NA, NA, NA, NA, "e6", NA, NA,
NA, NA, NA, NA, NA, NA,"varF1","cov",
NA, NA, NA, NA, NA, NA,"cov","varF2"),
byrow=TRUE, name="S" )
matrF <- mxMatrix( type="Full", nrow=6, ncol=8,
free=FALSE,
values=c(1,0,0,0,0,0,0,0,
0,1,0,0,0,0,0,0,
0,0,1,0,0,0,0,0,
0,0,0,1,0,0,0,0,
0,0,0,0,1,0,0,0,
0,0,0,0,0,1,0,0),
byrow=TRUE, name="F" )
matrM <- mxMatrix( type="Full", nrow=1, ncol=8,
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",
"meanx4","meanx5","meanx6",NA,NA),
name="M" )
exp <- mxExpectationRAM("A","S","F","M",
dimnames=c("x1","x2","x3","y1","y2","y3","F1","F2"))
funML <- mxFitFunctionML()
twoFactorModel <- mxModel("Two Factor Model Matrix Specification",
dataCov, matrA, matrS, matrF, matrM, exp, funML)
# 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)[["meanx4"]], 2.955, 0.01)
omxCheckCloseEnough(coef(twoFactorFit)[["meanx5"]], 2.956, 0.01)
omxCheckCloseEnough(coef(twoFactorFit)[["meanx6"]], 2.967, 0.01)
# Compare OpenMx results to Mx results
# -----------------------------------------------------------------------------
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