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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: BivariateSaturated_MatrixCovCholesky.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
# Matrix style model input - Covariance matrix data input
#
# RevisionHistory:
# Hermine Maes -- 2009.10.08 updated & reformatted
# Ross Gore -- 2011.06.15 added Model, Data & Field metadata
# -----------------------------------------------------------------------
#options(error = utils::recover)
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
# -----------------------------------------------------------------------------
bivSatModel5 <- mxModel("bivSat5",
mxMatrix(
type="Lower",
nrow=2,
ncol=2,
free = TRUE,
values=.5,
name="Chol"
),
mxAlgebra(
expression=Chol %*% t(Chol),
name="expCov"
),
mxData(
observed=cov(testData),
type="cov",
numObs=1000
),
mxFitFunctionML(),mxExpectationNormal(
covariance="expCov",
dimnames=selVars
)
)
bivSatFit5 <- mxRun(bivSatModel5)
EC5 <- mxEval(expCov, bivSatFit5)
LL5 <- mxEval(objective,bivSatFit5)
SL5 <- summary(bivSatFit5)$SaturatedLikelihood
Chi5 <- LL5-SL5
# example 5: Saturated Model with Cov Matrices and Matrix-Style Input
# -----------------------------------------------------------------------------
bivSatModel5m <- mxModel("bivSat5m",
mxMatrix(
type="Lower",
nrow=2,
ncol=2,
free = TRUE,
values=.5,
name="Chol"
),
mxAlgebra(
expression=Chol %*% t(Chol),
name="expCov"
),
mxMatrix(
type="Full",
nrow=1,
ncol=2,
free = TRUE,
values=c(0,0),
name="expMean"
),
mxData(
observed=cov(testData),
type="cov",
numObs=1000,
means=colMeans(testData)
),
mxFitFunctionML(),mxExpectationNormal(
covariance="expCov",
means="expMean",
dimnames=selVars
)
)
bivSatFit5m <- mxRun(bivSatModel5m)
EM5m <- mxEval(expMean, bivSatFit5m)
EC5m <- mxEval(expCov, bivSatFit5m)
LL5m <- mxEval(objective,bivSatFit5m);
SL5m <- summary(bivSatFit5m)$SaturatedLikelihood
Chi5m <- LL5m-SL5m
# example 5m: Saturated Model with Cov Matrices & Means and Matrix-Style Input
# -----------------------------------------------------------------------------
omxCheckCloseEnough(Chi5,-0.001,.001)
omxCheckCloseEnough(c(EC5),c(1.065, 0.475, 0.475, 0.929),.001)
# 5:CovMat Cholesky
# -------------------------------------
omxCheckCloseEnough(Chi5m,-0.001,.001)
omxCheckCloseEnough(c(EC5m),c(1.065, 0.475, 0.475, 0.929),.001)
omxCheckCloseEnough(c(EM5m),c(0.058, 0.006),.001)
# 5m:CovMPat Cholesky
# -------------------------------------
# Compare OpenMx results to Mx results
# (LL: likelihood; EC: expected covariance, EM: expected means)
# -----------------------------------------------------------------------------
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