1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
|
#
# 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: BivariateHeterogeneity_MatrixRaw.R
# Author: Hermine Maes
# Date: 2009.08.01
#
# ModelType: Heterogeneity
# DataType: Continuous
# Field: None
#
# Purpose:
# Bivariate Heterogeneity model to test differences in means and
# variances across multiple groups
# Matrix style model input - Raw data input
#
# RevisionHistory:
# Hermine Maes -- 2009.10.08 updated & reformatted
# Ross Gore -- 2011.06.15 added Model, Data & Field metadata
# Hermine Maes -- 2014.11.02 piecewise specification
# -----------------------------------------------------------------------------
require(OpenMx)
require(MASS)
# Load Libraries
# -----------------------------------------------------------------------------
set.seed(200)
rs=.5
xy1 <- mvtnorm::rmvnorm (1000, c(0,0), matrix(c(1,rs,rs,1),2,2))
xy1 <- xy1[, order(apply(xy1, 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.
# group 1
# --------------------------------------
set.seed(200)
rs=.4
xy2 <- mvtnorm::rmvnorm (1000, c(0,0), matrix(c(1,rs,rs,1),2,2))
xy2 <- xy2[, order(apply(xy2, 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.
# group 2
# --------------------------------------
# Simulate Data
# -----------------------------------------------------------------------------
selVars <- c("X","Y")
summary(xy1)
cov(xy1)
dimnames(xy1) <- list(NULL, selVars)
summary(xy2)
cov(xy2)
dimnames(xy2) <- list(NULL, selVars)
# Print Descriptive Statistics
# -----------------------------------------------------------------------------
chol1 <- mxMatrix( type="Lower", nrow=2, ncol=2,
free = TRUE, values=.5, labels=c("Ch11","Ch21","Ch31"),
name="chol1" )
expCov1 <- mxAlgebra( expression=chol1 %*% t(chol1), name="expCov1" )
expMean1 <- mxMatrix( type="Full", nrow=1, ncol=2,
free = TRUE, values=c(0,0), labels=c("mX1","mY1"),
name="expMean1" )
dataRaw1 <- mxData( xy1, type="raw" )
exp1 <- mxExpectationNormal( covariance="expCov1", means="expMean1", selVars)
funML <- mxFitFunctionML()
model1 <- mxModel("group1",
dataRaw1, chol1, expCov1, expMean1, exp1, funML)
chol2 <- mxMatrix( type="Lower", nrow=2, ncol=2,
free = TRUE, values=.5, labels=c("Ch12","Ch22","Ch32"),
name="chol2" )
expCov2 <- mxAlgebra( expression=chol2 %*% t(chol2), name="expCov2" )
expMean2 <- mxMatrix( type="Full", nrow=1, ncol=2,
free = TRUE, values=c(0,0), labels=c("mX2","mY2"),
name="expMean2" )
dataRaw2 <- mxData( xy2, type="raw" )
exp2 <- mxExpectationNormal( covariance="expCov2", means="expMean2", selVars)
funML <- mxFitFunctionML()
model2 <- mxModel("group2",
dataRaw2, chol2, expCov2, expMean2, exp2, funML)
fun <- mxFitFunctionMultigroup(c("group1", "group2"))
bivHetModel <- mxModel("bivariate Heterogeneity Matrix Specification",
model1, model2, fun )
bivHetFit <- mxRun(bivHetModel)
expMean1Het <- mxEval(group1.expMean1, bivHetFit)
expMean2Het <- mxEval(group2.expMean2, bivHetFit)
expCov1Het <- mxEval(group1.expCov1, bivHetFit)
expCov2Het <- mxEval(group2.expCov2, bivHetFit)
LLHet <- -2*logLik(bivHetFit)
expMean1Het; expMean2Het; expCov1Het; expCov2Het; LLHet
# Fit Heterogeneity Model
# -----------------------------------------------------------------------------
bivHomModel <- bivHetModel
bivHomModel[['group2.chol2']]$labels <- bivHomModel[['group1.chol1']]$labels
bivHomModel[['group2.expMean2']]$labels <- bivHomModel[['group1.expMean1']]$labels
bivHomFit <- mxRun(bivHomModel)
expMean1Hom <- mxEval(group1.expMean1, bivHomFit)
expMean2Hom <- mxEval(group2.expMean2, bivHomFit)
expCov1Hom <- mxEval(group1.expCov1, bivHomFit)
expCov2Hom <- mxEval(group2.expCov2, bivHomFit)
LLHom <- -2*logLik(bivHomFit)
expMean1Hom; expMean2Hom; expCov1Hom; expCov2Hom; LLHom
Chi = (LLHom - LLHet)
# LRT
rbind(LLHet, LLHom, Chi)
# =========================
# = Fit Homogeneity Model =
# =========================
omxCheckCloseEnough(LLHet, 10927.4024, .001)
omxCheckCloseEnough(c(expCov1Het), c(1.0656, 0.4752, 0.4752, 0.9292), .001)
omxCheckCloseEnough(c(expMean1Het), c(0.0582, 0.0063), .001)
omxCheckCloseEnough(c(expCov2Het), c(1.0728, 0.3739, 0.3739, 0.9283),.001)
omxCheckCloseEnough(c(expMean2Het), c(0.0596, 0.0028),.001)
omxCheckCloseEnough(LLHom, 10936.95,.001)
omxCheckCloseEnough(c(expCov1Hom), c(1.0692, 0.4245, 0.4245, 0.9287),.001)
omxCheckCloseEnough(c(expMean1Hom), c(0.0589, 0.0046),.001)
omxCheckCloseEnough(c(expCov2Hom), c(1.0692, 0.4245, 0.4245, 0.9287),.001)
omxCheckCloseEnough(c(expMean2Hom), c(0.0589, 0.0046),.001)
# Compare OpenMx results to Mx results
# (LL: likelihood; expCov: expected covariance, expMean: expected means)
# -----------------------------------------------------------------------------
|
