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
145
146
147
148
149
150
151
152
153
154
155
156
|
#
# Copyright 2007-2018 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.
#------------------------------------------------------------------------------
# Author: Michael D. Hunter
# Date: 2014.04.12
# Filename: MultilevelStateSpaceEx5.R
# Purpose: Replicate Mplus results reported by Gu et al. 2014 for a 2-level
# structural equation model. It's a factor model with "random intercepts".
#------------------------------------------------------------------------------
# Revision History
# Mon 21 Apr 2014 07:23:58 Central Daylight Time -- Michael Hunter added comments for file distribution to
# Steve Boker and Colleagues for Multilevel BG collaboration
#
#------------------------------------------------------------------------------
# Load Package, read in data, set a variable or two
require(OpenMx) #Note: must be r3345 or later
# Source of data
#http://www.infoagepub.com/products/content/files/serlinfiles_multilevel/Chapter%2010/Mplus/
# setwd("../Desktop")
# setwd("C:/Users/mhunter/Documents/Projects/OpenMx/MultilevelSSM")
# requires internet connection
data <- read.table("http://www.infoagepub.com/products/content/files/serlinfiles_multilevel/Chapter%2010/Mplus/Ch10Mplus.dat")
dataL <- list()
for(k in unique(data$V1)){
dataL[[k]] <- data[data$V1==k,]
}
nx <- 3
ny <- 3
nu <- 1
#mxOption(NULL, "Default optimizer", "NPSOL")
#------------------------------------------------------------------------------
# Specify and fit the model
# The WITHIN model
LW <- mxMatrix(name="LamW", "Full", ny, nu, values=1, labels=paste('lw', 1:ny, sep=''), free=c(FALSE, TRUE, TRUE))
PW <- mxMatrix(name="PsiW", "Full", nu, nu, values=1, free=TRUE, labels="psw")
TW <- mxMatrix(name="ThdW", "Diag", ny, ny, values=1, free=TRUE, labels=paste('thw', 1:ny, sep=''))
CW <- mxAlgebra(name="CovW", LamW %*% PsiW %*% t(LamW) + ThdW)
# The BETWEEN model
LB <- mxMatrix(name="LamB", "Full", nx, nu, values=1, labels=paste('lb', 1:ny, sep=''), free=c(FALSE, TRUE, TRUE))
PB <- mxMatrix(name="PsiB", "Full", nu, nu, values=1, free=TRUE, labels="psb")
TB <- mxMatrix(name="ThdB", "Diag", nx, nx, values=1, free=TRUE, labels=paste('thb', 1:ny, sep=''))
CB <- mxAlgebra(name="CovB", LamB %*% PsiB %*% t(LamB) + ThdB)
# The state space matrices
a <- mxMatrix(name="A", "Diag", nx, nx, values=1)
b <- mxMatrix(name="B", "Zero", nx, nu)
c <- mxMatrix(name="C", "Diag", ny, nx, values=1, dimnames=list(c('V2', 'V3', 'V4'), c('u_1', 'u_2', 'u_3')))
d <- mxMatrix(name="D", "Full", ny, nu, values=1, free=TRUE, labels=c('g100', 'g200', 'g300'))
q <- mxMatrix(name="Q", "Zero", nx, nx)
u <- mxMatrix(name="u", "Full", nu, 1, values=1)
x0 <- mxMatrix(name="x0", "Zero", nx, 1)
# Create a list of mxModels, one for each level 2 unit (classroom)
indivmodels <- list()
for(k in unique(data$V1)){
indivmodels[[k]] <- mxModel(name=paste('indiv', k, sep=''),
a, b, c, d, q, x0, u,
LW, PW, TW, CW, LB, PB, TB, CB,
mxExpectationStateSpace(A="A", B="B", C="C", D="D", Q="Q", R="CovW", x0="x0", P0="CovB", u="u"),
# note the R and P0 matrices
mxFitFunctionML(),
mxData(dataL[[k]], type='raw')) # note separate data
}
# There should be a slicker way to do this, but I haven't found it yet.
# I'd like to have one model where the SSM matrices live, one model for the WITHIN matrices,
# one model for the BETWEEN matrices, and then a list of models that refer to these, each with
# their own data. I guess that's what flattening is doing.
# Still I'd like to use built-in expectation functions to create the within/between
# expected covariance matrices.
groupfits <- paste("indiv", unique(data$V1), ".fitfunction", sep="")
m3s <- mxModel(model='Container', indivmodels, mxFitFunctionMultigroup(groupfits))
m3sRun <- mxRun(m3s)
summary(m3sRun) #runs in approx 60 seconds on my machine
# matches table 5
mplusParam <- c(3.677, 3.731, 3.706, .978, 1.070, 1.248, 1.769, 1.868, 1.510, 1.039, 1.091, .107, .025, .058, .037)
omxCheckCloseEnough(omxGetParameters(m3sRun), mplusParam, 0.001)
#Also check standard errors
mplusSE <- c(.073, .082, .080, .040, .044, .074, .063, .063, .065, .234, .228, .042, .019, .026, .023)
rd <- (summary(m3sRun)$parameters[,6] - mplusSE) / mplusSE
omxCheckCloseEnough(rd, rep(0, length(mplusSE)), 0.01)
#------------------------------------------------------------------------------
# Different way to do the same multilevel model.
# This way avoids the multigroup overhead.
# Instead of using multiple groups, it just re-initializes
# This example only re-initialized the covariances, bc the
# between cluster means are always zero.
# Create continue cluster variable
# 0 at the beginning of each cluster, 1 everywhere else.
dataC <- data
dataC$cclus <- c(0, 1-diff(dataC$V1))
a2 <- mxMatrix(name='A', 'Diag', nx, nx, labels='data.cclus')
sw <- mxMatrix(name='con', 'Full', 1, 1, labels='data.cclus')
q2 <- mxAlgebra((1-con) %x% CovB, name='Q')
simpleModel <- mxModel('SimpleMultilevel',
a2, b, c, d, q2, x0, u, sw,
LW, PW, TW, CW, LB, PB, TB, CB,
mxExpectationStateSpace(A="A", B="B", C="C", D="D", Q="Q", R="CovW", x0="x0", P0="CovB", u="u"),
# note the R and P0 matrices
mxFitFunctionML(),
mxData(dataC, type='raw')
)
simpleRun <- mxRun(simpleModel)
omxCheckCloseEnough(omxGetParameters(simpleRun), mplusParam, 0.001)
rd <- (summary(simpleRun)$parameters[,6] - mplusSE) / mplusSE
omxCheckCloseEnough(rd, rep(0, length(mplusSE)), 0.05)
|
