demo/BivariateSaturated.R
In OpenMx/OpenMx: Extended Structural Equation Modelling
#
# Copyright 2007-2021 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: BivariateSaturated.R
# Author: Hermine Maes
# Date: 2009.08.01
#
# ModelType: Saturated
# DataType: Continuous
# Field: None
#
# Purpose:
# Bivariate Saturated model to estimate means and (co)variances
# using Cholesky Decomposition
# Two matrix styles - Two data styles
#
# RevisionHistory:
# Hermine Maes -- 2009.10.08 updated & reformatted
# Ross Gore -- 2011.06.15 added Model, Data & Field metadata
# -----------------------------------------------------------------------
require(OpenMx)
require(MASS)
# Load Libraries
# -----------------------------------------------------------------------------
set.seed(200)
rs=.5
xy <- mvtnorm::rmvnorm (1000, c(0,0), matrix(c(1,rs,rs,1),2,2))
testData <- xy
testData <- testData[, order(apply(testData, 2, var))[2:1]] #put the data columns in order from largest to smallest variance
# Note: Users do NOT have to re-order their data columns. This is only to make data generation the same on different operating systems: to fix an inconsistency with the mvtnorm::rmvnorm function in the MASS package.
selVars <- c('X','Y')
dimnames(testData) <- list(NULL, selVars)
summary(testData)
cov(testData)
# Simulate Data
# -----------------------------------------------------------------------------
bivSatModel1 <- mxModel("bivSat1",
manifestVars= selVars,
mxPath(
from=c("X", "Y"),
arrows=2,
free = TRUE,
values=1,
lbound=.01,
labels=c("varX","varY")
),
mxPath(
from="X",
to="Y",
arrows=2,
free = TRUE,
values=.2,
lbound=.01,
labels="covXY"
),
mxData(
observed=cov(testData),
type="cov",
numObs=1000
),
type="RAM"
)
bivSatFit1 <- mxRun(bivSatModel1)
EC1 <- mxEval(S, bivSatFit1)
LL1 <- mxEval(fitfunction, bivSatFit1)
SL1 <- summary(bivSatFit1)$SaturatedLikelihood
Chi1 <- LL1-SL1
# example 1: Saturated Model with Cov Matrices and Path-Style Input
# -----------------------------------------------------------------------------
bivSatModel1m <- mxModel("bivSat1m",
manifestVars= selVars,
mxPath(
from=c("X", "Y"),
arrows=2,
free = TRUE,
values=1,
lbound=.01,
labels=c("varX","varY")
),
mxPath(
from="X",
to="Y",
arrows=2,
free = TRUE,
values=.2,
lbound=.01,
labels="covXY"
),
mxPath(
from="one",
to=c("X", "Y"),
arrows=1,
free = TRUE,
values=.01,
labels=c("meanX","meanY")
),
mxData(
observed=cov(testData),
type="cov",
numObs=1000,
means=colMeans(testData)
),
type="RAM"
)
bivSatFit1m <- mxRun(bivSatModel1m)
EM1m <- mxEval(M, bivSatFit1m)
EC1m <- mxEval(S, bivSatFit1m)
LL1m <- mxEval(fitfunction, bivSatFit1m)
SL1m <- summary(bivSatFit1m)$SaturatedLikelihood
Chi1m <- LL1m-SL1m
# example 1m: Saturated Model with Cov Matrices & Means and Path-Style Input
# -----------------------------------------------------------------------------
bivSatModel2 <- mxModel("bivSat2",
manifestVars= selVars,
mxPath(
from=c("X", "Y"),
arrows=2,
free = TRUE,
values=1,
lbound=.01,
labels=c("varX","varY")
),
mxPath(
from="X",
to="Y",
arrows=2,
free = TRUE,
values=.2,
lbound=.01,
labels="covXY"
),
mxPath(from="one",
to=c("X", "Y"),
arrows=1,
free=T),
mxData(
observed=testData,
type="raw",
),
type="RAM"
)
bivSatFit2 <- mxRun(bivSatModel2)
EM2 <- mxEval(M, bivSatFit2)
EC2 <- mxEval(S, bivSatFit2)
LL2 <- mxEval(fitfunction, bivSatFit2)
SL2 <- summary(bivSatFit1)$SaturatedLikelihood
Chi2 <- LL2-SL2
# example 2: Saturated Model with Raw Data and Path input
# -----------------------------------------------------------------------------
bivSatModel2s <- mxModel(bivSatModel1,
mxData(
observed=testData,
type="raw",
),
mxPath(from="one",
to=c("X", "Y"),
arrows=1,
free=T),
name = "bivSat2s"
)
bivSatFit2s <- mxRun(bivSatModel2s)
EM2s <- mxEval(M, bivSatFit2s)
EC2s <- mxEval(S, bivSatFit2s)
LL2s <- mxEval(fitfunction, bivSatFit2s)
# example 2s: Saturated Model with Raw Data and Path input built upon Cov/Means version
# -----------------------------------------------------------------------------
bivSatModel3 <- mxModel("bivSat3",
mxMatrix(
type="Symm",
nrow=2,
ncol=2,
free = TRUE,
values=c(1,.5,1),
dimnames=list(selVars,selVars),
name="expCov"
),
mxData(
observed=cov(testData),
type="cov",
numObs=1000
),
mxExpectationNormal(
covariance="expCov"
),
mxFitFunctionML()
)
bivSatFit3 <- mxRun(bivSatModel3)
EC3 <- mxEval(expCov, bivSatFit3)
LL3 <- mxEval(fitfunction,bivSatFit3)
SL3 <- summary(bivSatFit3)$SaturatedLikelihood
Chi3 <- LL3-SL3
# example 3: Saturated Model with Cov Matrices and Matrix-Style Input
# -----------------------------------------------------------------------------
bivSatModel3m <- mxModel("bivSat3m",
mxMatrix(
type="Symm",
nrow=2,
ncol=2,
free = TRUE,
values=c(1,.5,1),
name="expCov"
),
mxMatrix(
type="Full",
nrow=1,
ncol=2,
free = TRUE,
values=c(0,0),
name="expMean"
),
mxData(
observed=cov(testData),
type="cov",
numObs=1000,
means=colMeans(testData)
),
mxExpectationNormal(
covariance="expCov",
means="expMean",
dimnames=selVars
),
mxFitFunctionML()
)
bivSatFit3m <- mxRun(bivSatModel3m)
EM3m <- mxEval(expMean, bivSatFit3m)
EC3m <- mxEval(expCov, bivSatFit3m)
LL3m <- mxEval(fitfunction,bivSatFit3m)
SL3m <- summary(bivSatFit3m)$SaturatedLikelihood
Chi3m <- LL3m-SL3m
# example 3m: Saturated Model with Cov Matrices & Means and Matrix-Style Input
# -----------------------------------------------------------------------------
bivSatModel4 <- mxModel("bivSat4",
mxMatrix(
type="Symm",
nrow=2,
ncol=2,
free = TRUE,
values=c(1,.5,1),
name="expCov"
),
mxMatrix(
type="Full",
nrow=1,
ncol=2,
free = TRUE,
values=c(0,0),
name="expMean"
),
mxData(
observed=testData,
type="raw",
),
mxExpectationNormal(
covariance="expCov",
means="expMean",
dimnames=selVars
),
mxFitFunctionML()
)
bivSatFit4 <- mxRun(bivSatModel4)
EM4 <- mxEval(expMean, bivSatFit4)
EC4 <- mxEval(expCov, bivSatFit4)
LL4 <- mxEval(fitfunction,bivSatFit4)
# examples 4: Saturated Model with Raw Data and Matrix-Style Input
# -----------------------------------------------------------------------------
bivSatModel5 <- mxModel("bivSat5",
mxMatrix(
type="Full",
nrow=2,
ncol=2,
free=c(T,T,F,T),
values=c(1,.2,0,1),
name="Chol"
),
mxAlgebra(
Chol %*% t(Chol),
name="expCov",
dimnames=list(selVars,selVars)
),
mxMatrix(
type="Full",
nrow=1,
ncol=2,
free = TRUE,
values=c(0,0),
dimnames=list(NULL,selVars),
name="expMean"
),
mxData(
observed=cov(testData),
type="cov",
numObs=1000
),
mxExpectationNormal(
covariance="expCov"
),
mxFitFunctionML()
)
bivSatFit5 <- omxCheckWarning(mxRun(bivSatModel5),
"Hessian at the solution does not appear to be convex.")
EC5 <- mxEval(expCov, bivSatFit5)
LL5 <- mxEval(fitfunction,bivSatFit5)
SL5 <- summary(bivSatFit5)$SaturatedLikelihood
Chi5 <- LL5-SL5
# example 5: Saturated Model with Cov Matrices and Matrix-Style Input
# -----------------------------------------------------------------------------
bivSatModel5m <- mxModel("bivSat5m",
mxMatrix(
type="Full",
nrow=2,
ncol=2,
free=c(T,T,F,T),
values=c(1,.2,0,1),
name="Chol"
),
mxAlgebra(
Chol %*% t(Chol),
name="expCov",
dimnames=list(selVars,selVars)
),
mxMatrix(
type="Full",
nrow=1,
ncol=2,
free = TRUE,
values=c(0,0),
dimnames=list(NULL,selVars),
name="expMean"
),
mxData(
observed=cov(testData),
type="cov",
numObs=1000,
means=colMeans(testData)
),
mxExpectationNormal(
covariance="expCov",
means="expMean"
),
mxFitFunctionML()
)
bivSatFit5m <- mxRun(bivSatModel5m)
EM5m <- mxEval(expMean, bivSatFit5m)
EC5m <- mxEval(expCov, bivSatFit5m)
LL5m <- mxEval(fitfunction,bivSatFit5m);
SL5m <- summary(bivSatFit5m)$SaturatedLikelihood
Chi5m <- LL5m-SL5m
# example 5m: Saturated Model with Cov Matrices & Means and Matrix-Style Input
# -----------------------------------------------------------------------------
bivSatModel6 <- mxModel("bivSat6",
mxMatrix(
type="Full",
nrow=2,
ncol=2,
free=c(T,T,F,T),
values=c(1,.2,0,1),
name="Chol"
),
mxAlgebra(
Chol %*% t(Chol),
name="expCov",
dimnames=list(selVars,selVars)
),
mxMatrix(
type="Full",
nrow=1,
ncol=2,
free = TRUE,
values=c(0,0),
dimnames=list(NULL,selVars),
name="expMean"
),
mxData(
observed=testData,
type="raw",
),
mxExpectationNormal(
covariance="expCov",
means="expMean"
),
mxFitFunctionML()
)
bivSatFit6 <- mxRun(bivSatModel6)
EM6 <- mxEval(expMean, bivSatFit6)
EC6 <- mxEval(expCov, bivSatFit6)
LL6 <- mxEval(fitfunction,bivSatFit6)
# examples 6: Saturated Model with RawData and Matrix-Style Input
# -----------------------------------------------------------------------------
omxCheckCloseEnough(Chi1, 0,.01)
omxCheckCloseEnough(c(EC1), c(1.0656, 0.4751, 0.4751, 0.9291),.001)
#1:CovPat
# -------------------------------------
omxCheckCloseEnough(Chi1m, 0,.01)
omxCheckCloseEnough(c(EC1m), c(1.0656, 0.4751, 0.4751, 0.9291),.001)
omxCheckCloseEnough(c(EM1m), c(0.0582, 0.0063), .001)
#1m:CovMPat
# -------------------------------------
omxCheckCloseEnough(LL2, 5407.037,.01)
omxCheckCloseEnough(c(EC2), c(1.0656, 0.4752, 0.4752, 0.9292),.001)
omxCheckCloseEnough(c(EM2), c(0.0582, 0.0063), .001)
#2:RawPat
# -------------------------------------
omxCheckCloseEnough(LL2s, 5407.037, .01)
omxCheckCloseEnough(c(EC2s), c(1.0656, 0.4752, 0.4752, 0.9292),.001)
omxCheckCloseEnough(c(EM2s), c(0.0582, 0.0063),.001)
#2:RawSPat
# -------------------------------------
omxCheckCloseEnough(Chi3, 0,.01)
omxCheckCloseEnough(c(EC3),c(1.0656, 0.4752, 0.4752, 0.9292),.001)
#3:CovMat
# -------------------------------------
omxCheckCloseEnough(Chi3m,0,.01)
omxCheckCloseEnough(c(EC3m),c(1.0656, 0.4752, 0.4752, 0.9292),.001)
omxCheckCloseEnough(c(EM3m),c(0.058, 0.006),.001)
#3m:CovMPat
# -------------------------------------
omxCheckCloseEnough(LL4,5407.037,.01)
omxCheckCloseEnough(c(EC4),c(1.066, 0.475, 0.475, 0.929),.001)
omxCheckCloseEnough(c(EM4),c(0.058, 0.006),.001)
#4:RawMat
# -------------------------------------
omxCheckCloseEnough(Chi5,0,.01)
omxCheckCloseEnough(c(EC5),c(1.0656, 0.4752, 0.4752, 0.9292),.001)
#5:CovMat Cholesky
# -------------------------------------
omxCheckCloseEnough(Chi5m,0,.01)
omxCheckCloseEnough(c(EC5m),c(1.0656, 0.4752, 0.4752, 0.9292),.001)
omxCheckCloseEnough(c(EM5m),c(0.058, 0.006),.001)
#5m:CovMPat Cholesky
# -------------------------------------
omxCheckCloseEnough(LL6,5407.037,.01)
omxCheckCloseEnough(c(EC6),c(1.066, 0.475, 0.475, 0.929),.001)
omxCheckCloseEnough(c(EM6),c(0.058, 0.006),.001)
#6:RawMat Cholesky
# -------------------------------------
# Compare OpenMx results to Mx results
# (LL: likelihood; EC: expected covariance, EM: expected means)
# -----------------------------------------------------------------------
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#
# Copyright 2007-2021 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: BivariateSaturated.R
# Author: Hermine Maes
# Date: 2009.08.01
#
# ModelType: Saturated
# DataType: Continuous
# Field: None
#
# Purpose:
# Bivariate Saturated model to estimate means and (co)variances
# using Cholesky Decomposition
# Two matrix styles - Two data styles
#
# RevisionHistory:
# Hermine Maes -- 2009.10.08 updated & reformatted
# Ross Gore -- 2011.06.15 added Model, Data & Field metadata
# -----------------------------------------------------------------------
require(OpenMx)
require(MASS)
# Load Libraries
# -----------------------------------------------------------------------------
set.seed(200)
rs=.5
xy <- mvtnorm::rmvnorm (1000, c(0,0), matrix(c(1,rs,rs,1),2,2))
testData <- xy
testData <- testData[, order(apply(testData, 2, var))[2:1]] #put the data columns in order from largest to smallest variance
# Note: Users do NOT have to re-order their data columns. This is only to make data generation the same on different operating systems: to fix an inconsistency with the mvtnorm::rmvnorm function in the MASS package.
selVars <- c('X','Y')
dimnames(testData) <- list(NULL, selVars)
summary(testData)
cov(testData)
# Simulate Data
# -----------------------------------------------------------------------------
bivSatModel1 <- mxModel("bivSat1",
manifestVars= selVars,
mxPath(
from=c("X", "Y"),
arrows=2,
free = TRUE,
values=1,
lbound=.01,
labels=c("varX","varY")
),
mxPath(
from="X",
to="Y",
arrows=2,
free = TRUE,
values=.2,
lbound=.01,
labels="covXY"
),
mxData(
observed=cov(testData),
type="cov",
numObs=1000
),
type="RAM"
)
bivSatFit1 <- mxRun(bivSatModel1)
EC1 <- mxEval(S, bivSatFit1)
LL1 <- mxEval(fitfunction, bivSatFit1)
SL1 <- summary(bivSatFit1)$SaturatedLikelihood
Chi1 <- LL1-SL1
# example 1: Saturated Model with Cov Matrices and Path-Style Input
# -----------------------------------------------------------------------------
bivSatModel1m <- mxModel("bivSat1m",
manifestVars= selVars,
mxPath(
from=c("X", "Y"),
arrows=2,
free = TRUE,
values=1,
lbound=.01,
labels=c("varX","varY")
),
mxPath(
from="X",
to="Y",
arrows=2,
free = TRUE,
values=.2,
lbound=.01,
labels="covXY"
),
mxPath(
from="one",
to=c("X", "Y"),
arrows=1,
free = TRUE,
values=.01,
labels=c("meanX","meanY")
),
mxData(
observed=cov(testData),
type="cov",
numObs=1000,
means=colMeans(testData)
),
type="RAM"
)
bivSatFit1m <- mxRun(bivSatModel1m)
EM1m <- mxEval(M, bivSatFit1m)
EC1m <- mxEval(S, bivSatFit1m)
LL1m <- mxEval(fitfunction, bivSatFit1m)
SL1m <- summary(bivSatFit1m)$SaturatedLikelihood
Chi1m <- LL1m-SL1m
# example 1m: Saturated Model with Cov Matrices & Means and Path-Style Input
# -----------------------------------------------------------------------------
bivSatModel2 <- mxModel("bivSat2",
manifestVars= selVars,
mxPath(
from=c("X", "Y"),
arrows=2,
free = TRUE,
values=1,
lbound=.01,
labels=c("varX","varY")
),
mxPath(
from="X",
to="Y",
arrows=2,
free = TRUE,
values=.2,
lbound=.01,
labels="covXY"
),
mxPath(from="one",
to=c("X", "Y"),
arrows=1,
free=T),
mxData(
observed=testData,
type="raw",
),
type="RAM"
)
bivSatFit2 <- mxRun(bivSatModel2)
EM2 <- mxEval(M, bivSatFit2)
EC2 <- mxEval(S, bivSatFit2)
LL2 <- mxEval(fitfunction, bivSatFit2)
SL2 <- summary(bivSatFit1)$SaturatedLikelihood
Chi2 <- LL2-SL2
# example 2: Saturated Model with Raw Data and Path input
# -----------------------------------------------------------------------------
bivSatModel2s <- mxModel(bivSatModel1,
mxData(
observed=testData,
type="raw",
),
mxPath(from="one",
to=c("X", "Y"),
arrows=1,
free=T),
name = "bivSat2s"
)
bivSatFit2s <- mxRun(bivSatModel2s)
EM2s <- mxEval(M, bivSatFit2s)
EC2s <- mxEval(S, bivSatFit2s)
LL2s <- mxEval(fitfunction, bivSatFit2s)
# example 2s: Saturated Model with Raw Data and Path input built upon Cov/Means version
# -----------------------------------------------------------------------------
bivSatModel3 <- mxModel("bivSat3",
mxMatrix(
type="Symm",
nrow=2,
ncol=2,
free = TRUE,
values=c(1,.5,1),
dimnames=list(selVars,selVars),
name="expCov"
),
mxData(
observed=cov(testData),
type="cov",
numObs=1000
),
mxExpectationNormal(
covariance="expCov"
),
mxFitFunctionML()
)
bivSatFit3 <- mxRun(bivSatModel3)
EC3 <- mxEval(expCov, bivSatFit3)
LL3 <- mxEval(fitfunction,bivSatFit3)
SL3 <- summary(bivSatFit3)$SaturatedLikelihood
Chi3 <- LL3-SL3
# example 3: Saturated Model with Cov Matrices and Matrix-Style Input
# -----------------------------------------------------------------------------
bivSatModel3m <- mxModel("bivSat3m",
mxMatrix(
type="Symm",
nrow=2,
ncol=2,
free = TRUE,
values=c(1,.5,1),
name="expCov"
),
mxMatrix(
type="Full",
nrow=1,
ncol=2,
free = TRUE,
values=c(0,0),
name="expMean"
),
mxData(
observed=cov(testData),
type="cov",
numObs=1000,
means=colMeans(testData)
),
mxExpectationNormal(
covariance="expCov",
means="expMean",
dimnames=selVars
),
mxFitFunctionML()
)
bivSatFit3m <- mxRun(bivSatModel3m)
EM3m <- mxEval(expMean, bivSatFit3m)
EC3m <- mxEval(expCov, bivSatFit3m)
LL3m <- mxEval(fitfunction,bivSatFit3m)
SL3m <- summary(bivSatFit3m)$SaturatedLikelihood
Chi3m <- LL3m-SL3m
# example 3m: Saturated Model with Cov Matrices & Means and Matrix-Style Input
# -----------------------------------------------------------------------------
bivSatModel4 <- mxModel("bivSat4",
mxMatrix(
type="Symm",
nrow=2,
ncol=2,
free = TRUE,
values=c(1,.5,1),
name="expCov"
),
mxMatrix(
type="Full",
nrow=1,
ncol=2,
free = TRUE,
values=c(0,0),
name="expMean"
),
mxData(
observed=testData,
type="raw",
),
mxExpectationNormal(
covariance="expCov",
means="expMean",
dimnames=selVars
),
mxFitFunctionML()
)
bivSatFit4 <- mxRun(bivSatModel4)
EM4 <- mxEval(expMean, bivSatFit4)
EC4 <- mxEval(expCov, bivSatFit4)
LL4 <- mxEval(fitfunction,bivSatFit4)
# examples 4: Saturated Model with Raw Data and Matrix-Style Input
# -----------------------------------------------------------------------------
bivSatModel5 <- mxModel("bivSat5",
mxMatrix(
type="Full",
nrow=2,
ncol=2,
free=c(T,T,F,T),
values=c(1,.2,0,1),
name="Chol"
),
mxAlgebra(
Chol %*% t(Chol),
name="expCov",
dimnames=list(selVars,selVars)
),
mxMatrix(
type="Full",
nrow=1,
ncol=2,
free = TRUE,
values=c(0,0),
dimnames=list(NULL,selVars),
name="expMean"
),
mxData(
observed=cov(testData),
type="cov",
numObs=1000
),
mxExpectationNormal(
covariance="expCov"
),
mxFitFunctionML()
)
bivSatFit5 <- omxCheckWarning(mxRun(bivSatModel5),
"Hessian at the solution does not appear to be convex.")
EC5 <- mxEval(expCov, bivSatFit5)
LL5 <- mxEval(fitfunction,bivSatFit5)
SL5 <- summary(bivSatFit5)$SaturatedLikelihood
Chi5 <- LL5-SL5
# example 5: Saturated Model with Cov Matrices and Matrix-Style Input
# -----------------------------------------------------------------------------
bivSatModel5m <- mxModel("bivSat5m",
mxMatrix(
type="Full",
nrow=2,
ncol=2,
free=c(T,T,F,T),
values=c(1,.2,0,1),
name="Chol"
),
mxAlgebra(
Chol %*% t(Chol),
name="expCov",
dimnames=list(selVars,selVars)
),
mxMatrix(
type="Full",
nrow=1,
ncol=2,
free = TRUE,
values=c(0,0),
dimnames=list(NULL,selVars),
name="expMean"
),
mxData(
observed=cov(testData),
type="cov",
numObs=1000,
means=colMeans(testData)
),
mxExpectationNormal(
covariance="expCov",
means="expMean"
),
mxFitFunctionML()
)
bivSatFit5m <- mxRun(bivSatModel5m)
EM5m <- mxEval(expMean, bivSatFit5m)
EC5m <- mxEval(expCov, bivSatFit5m)
LL5m <- mxEval(fitfunction,bivSatFit5m);
SL5m <- summary(bivSatFit5m)$SaturatedLikelihood
Chi5m <- LL5m-SL5m
# example 5m: Saturated Model with Cov Matrices & Means and Matrix-Style Input
# -----------------------------------------------------------------------------
bivSatModel6 <- mxModel("bivSat6",
mxMatrix(
type="Full",
nrow=2,
ncol=2,
free=c(T,T,F,T),
values=c(1,.2,0,1),
name="Chol"
),
mxAlgebra(
Chol %*% t(Chol),
name="expCov",
dimnames=list(selVars,selVars)
),
mxMatrix(
type="Full",
nrow=1,
ncol=2,
free = TRUE,
values=c(0,0),
dimnames=list(NULL,selVars),
name="expMean"
),
mxData(
observed=testData,
type="raw",
),
mxExpectationNormal(
covariance="expCov",
means="expMean"
),
mxFitFunctionML()
)
bivSatFit6 <- mxRun(bivSatModel6)
EM6 <- mxEval(expMean, bivSatFit6)
EC6 <- mxEval(expCov, bivSatFit6)
LL6 <- mxEval(fitfunction,bivSatFit6)
# examples 6: Saturated Model with RawData and Matrix-Style Input
# -----------------------------------------------------------------------------
omxCheckCloseEnough(Chi1, 0,.01)
omxCheckCloseEnough(c(EC1), c(1.0656, 0.4751, 0.4751, 0.9291),.001)
#1:CovPat
# -------------------------------------
omxCheckCloseEnough(Chi1m, 0,.01)
omxCheckCloseEnough(c(EC1m), c(1.0656, 0.4751, 0.4751, 0.9291),.001)
omxCheckCloseEnough(c(EM1m), c(0.0582, 0.0063), .001)
#1m:CovMPat
# -------------------------------------
omxCheckCloseEnough(LL2, 5407.037,.01)
omxCheckCloseEnough(c(EC2), c(1.0656, 0.4752, 0.4752, 0.9292),.001)
omxCheckCloseEnough(c(EM2), c(0.0582, 0.0063), .001)
#2:RawPat
# -------------------------------------
omxCheckCloseEnough(LL2s, 5407.037, .01)
omxCheckCloseEnough(c(EC2s), c(1.0656, 0.4752, 0.4752, 0.9292),.001)
omxCheckCloseEnough(c(EM2s), c(0.0582, 0.0063),.001)
#2:RawSPat
# -------------------------------------
omxCheckCloseEnough(Chi3, 0,.01)
omxCheckCloseEnough(c(EC3),c(1.0656, 0.4752, 0.4752, 0.9292),.001)
#3:CovMat
# -------------------------------------
omxCheckCloseEnough(Chi3m,0,.01)
omxCheckCloseEnough(c(EC3m),c(1.0656, 0.4752, 0.4752, 0.9292),.001)
omxCheckCloseEnough(c(EM3m),c(0.058, 0.006),.001)
#3m:CovMPat
# -------------------------------------
omxCheckCloseEnough(LL4,5407.037,.01)
omxCheckCloseEnough(c(EC4),c(1.066, 0.475, 0.475, 0.929),.001)
omxCheckCloseEnough(c(EM4),c(0.058, 0.006),.001)
#4:RawMat
# -------------------------------------
omxCheckCloseEnough(Chi5,0,.01)
omxCheckCloseEnough(c(EC5),c(1.0656, 0.4752, 0.4752, 0.9292),.001)
#5:CovMat Cholesky
# -------------------------------------
omxCheckCloseEnough(Chi5m,0,.01)
omxCheckCloseEnough(c(EC5m),c(1.0656, 0.4752, 0.4752, 0.9292),.001)
omxCheckCloseEnough(c(EM5m),c(0.058, 0.006),.001)
#5m:CovMPat Cholesky
# -------------------------------------
omxCheckCloseEnough(LL6,5407.037,.01)
omxCheckCloseEnough(c(EC6),c(1.066, 0.475, 0.475, 0.929),.001)
omxCheckCloseEnough(c(EM6),c(0.058, 0.006),.001)
#6:RawMat Cholesky
# -------------------------------------
# Compare OpenMx results to Mx results
# (LL: likelihood; EC: expected covariance, EM: expected means)
# -----------------------------------------------------------------------
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