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#
# 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.
# -----------------------------------------------------------------------
# Program: UnivariateTwinAnalysis_MatrixRaw.R
# Author: Hermine Maes
# Date: 08 01 2009
#
# Univariate Twin Analysis model to estimate causes of variation (ACE)
# Matrix style model input - Raw data input
#
# Revision History
# Hermine Maes -- 10 08 2009 updated & reformatted
# -----------------------------------------------------------------------
require(OpenMx)
#Prepare Data
# -----------------------------------------------------------------------
data(twinData)
summary(twinData)
selVars <- c('bmi1','bmi2')
mzfData <- as.matrix(subset(twinData, zyg==1, c(bmi1,bmi2)))
dzfData <- as.matrix(subset(twinData, zyg==3, c(bmi1,bmi2)))
colMeans(mzfData,na.rm=TRUE)
colMeans(dzfData,na.rm=TRUE)
cov(mzfData,use="complete")
cov(dzfData,use="complete")
#Fit ACE Model with RawData and Matrices Input
# -----------------------------------------------------------------------
twinACEModel <- mxModel("twinACE",
# Matrices X, Y, and Z to store a, c, and e path coefficients
mxMatrix(
type="Full",
nrow=1,
ncol=1,
free=TRUE,
values=.6,
label="a",
name="X"
),
mxMatrix(
type="Full",
nrow=1,
ncol=1,
free=TRUE,
values=.6,
label="c",
name="Y"
),
mxMatrix(
type="Full",
nrow=1,
ncol=1,
free=TRUE,
values=.6,
label="e",
name="Z"
),
# Matrices A, C, and E compute variance components
mxAlgebra(
expression=X %*% t(X),
name="A"
),
mxAlgebra(
expression=Y %*% t(Y),
name="C"
),
mxAlgebra(
expression=Z %*% t(Z),
name="E"
),
mxMatrix(
type="Full",
nrow=1,
ncol=2,
free=TRUE,
values= 20,
label="mean",
name="expMean"
),
# Algebra for expected variance/covariance matrix in MZ
mxAlgebra(
expression= rbind (cbind(A+C+E , A+C),
cbind(A+C , A+C+E)),
name="expCovMZ"
),
# Algebra for expected variance/covariance matrix in DZ
# note use of 0.5, converted to 1*1 matrix
mxAlgebra(
expression= rbind (cbind(A+C+E , 0.5%x%A+C),
cbind(0.5%x%A+C , A+C+E)),
name="expCovDZ"
),
mxModel("MZ",
mxData(
observed=mzfData,
type="raw"
),
mxExpectationNormal(
covariance="twinACE.expCovMZ",
means="twinACE.expMean",
dimnames=selVars
),
mxFitFunctionML(vector=TRUE)
),
mxModel("DZ",
mxData(
observed=dzfData,
type="raw"
),
mxFitFunctionML(),mxExpectationNormal(
covariance="twinACE.expCovDZ",
means="twinACE.expMean",
dimnames=selVars
),
mxFitFunctionML(vector=TRUE)
),
mxAlgebra(
expression=-2.0 *sum(log(MZ.objective), log(DZ.objective)),
name="twin"
),
mxFitFunctionAlgebra("twin")
)
#Run ACE model
# -----------------------------------------------------------------------
twinACEFit <- mxRun(twinACEModel)
MZc <- mxEval(expCovMZ, twinACEFit) # expected covariance matrix for MZ's
DZc <- mxEval(expCovDZ, twinACEFit) # expected covariance matrix for DZ's
M <- mxEval(expMean, twinACEFit) # expected mean
A <- mxEval(a*a, twinACEFit) # additive genetic variance, a^2
C <- mxEval(c*c, twinACEFit) # shared environmental variance, c^2
E <- mxEval(e*e, twinACEFit) # unique environmental variance, e^2
V <- (A+C+E) # total variance
a2 <- A/V # standardized additive genetic variance
c2 <- C/V # standardized shared environmental variance
e2 <- E/V # standardized unique environmental variance
ACEest <- rbind(cbind(A,C,E),cbind(a2,c2,e2)) # table of estimates
LL_ACE <- mxEval(objective, twinACEFit) # likelihood of ACE model
#Mx answers hard-coded
# -----------------------------------------------------------------------
#1: Heterogeneity Model
Mx.A <- 0.6173023
Mx.C <- 5.595822e-14
Mx.E <- 0.1730462
Mx.M <- matrix(c(21.39293, 21.39293),1,2)
Mx.LL_ACE <- 4067.663
#Compare OpenMx results to Mx results (LL: likelihood; EC: expected covariance, EM: expected means)
# -----------------------------------------------------------------------
omxCheckCloseEnough(LL_ACE,Mx.LL_ACE,.001)
omxCheckCloseEnough(A,Mx.A,.001)
omxCheckCloseEnough(C,Mx.C,.001)
omxCheckCloseEnough(E,Mx.E,.001)
omxCheckCloseEnough(M,Mx.M,.001)
#Run AE model
# -----------------------------------------------------------------------
twinAEModel <- mxModel(twinACEModel, #name = "twinAE",
# drop c at 0
mxMatrix(
type="Full",
nrow=1,
ncol=1,
free=FALSE,
values=0,
label="c",
name="Y"
)
)
twinAEFit <- mxRun(twinAEModel)
MZc <- mxEval(expCovMZ, twinAEFit)
DZc <- mxEval(expCovDZ, twinAEFit)
M <- mxEval(expMean, twinAEFit)
A <- mxEval(a*a, twinAEFit)
C <- mxEval(c*c, twinAEFit)
E <- mxEval(e*e, twinAEFit)
V <- (A+C+E)
a2 <- A/V
c2 <- C/V
e2 <- E/V
AEest <- rbind(cbind(A,C,E),cbind(a2,c2,e2))
LL_AE <- mxEval(objective, twinAEFit)
#Mx answers hard-coded
# -----------------------------------------------------------------------
#1: Homogeneity Model
Mx.A <- 0.6173023
Mx.C <- 0
Mx.E <- 0.1730462
Mx.M <- matrix(c(21.39293, 21.39293),1,2)
Mx.LL_AE <- 4067.663
#Compare OpenMx results to Mx results
# -----------------------------------------------------------------------
# (LL: likelihood; EC: expected covariance, EM: expected means)
omxCheckCloseEnough(LL_AE,Mx.LL_AE,.001)
omxCheckCloseEnough(A,Mx.A,.001)
omxCheckCloseEnough(C,Mx.C,.001)
omxCheckCloseEnough(E,Mx.E,.001)
omxCheckCloseEnough(M,Mx.M,.001)
LRT_ACE_AE <- LL_AE - LL_ACE
#Print relevant output
# -----------------------------------------------------------------------
ACEest
AEest
LRT_ACE_AE
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