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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.R
# Author: Hermine Maes
# Date: 2009.08.01
#
# ModelType: ACE
# DataType: Simulated Twin
# Field: Human Behavior Genetics
#
# Purpose:
# Univariate Twin Analysis Example in OpenMx:
# From fitting saturated models to testing model assumptions
# To fitting the ACE model and a submodel
#
# RevisionHistory:
# Hermine Maes -- 10 08 2009 updated & reformatted
# Ross Gore -- 06 06 2011 added Model, Data & Field metadata
# -----------------------------------------------------------------------
require(OpenMx)
require(MASS)
# Load Library
# -----------------------------------------------------------------------
set.seed(200)
a2<-0.5 #Additive genetic variance component (a squared)
c2<-0.3 #Common environment variance component (c squared)
e2<-0.2 #Specific environment variance component (e squared)
rMZ <- a2+c2
rDZ <- .5*a2+c2
DataMZ <- mvtnorm::rmvnorm (1000, c(0,0), matrix(c(1,rMZ,rMZ,1),2,2))
DataDZ <- mvtnorm::rmvnorm (1000, c(0,0), matrix(c(1,rDZ,rDZ,1),2,2))
selVars <- c('t1','t2')
dimnames(DataMZ) <- list(NULL,selVars)
dimnames(DataDZ) <- list(NULL,selVars)
summary(DataMZ)
summary(DataDZ)
colMeans(DataMZ,na.rm=TRUE)
colMeans(DataDZ,na.rm=TRUE)
cov(DataMZ,use="complete")
cov(DataDZ,use="complete")
# Simulate Data: two standardized variables t1 & t2 for MZ's & DZ's
# -----------------------------------------------------------------------
twinSatModel <- mxModel("twinSat",
mxModel("MZ",
mxMatrix("Full", 1, 2, T, c(0,0), name="expMeanMZ"),
mxMatrix("Lower", 2, 2, T, .5, name="CholMZ"),
mxAlgebra(CholMZ %*% t(CholMZ), name="expCovMZ"),
mxData(DataMZ, type="raw"),
mxFitFunctionML(),mxExpectationNormal("expCovMZ", "expMeanMZ", selVars)),
mxModel("DZ",
mxMatrix("Full", 1, 2, T, c(0,0), name="expMeanDZ"),
mxMatrix("Lower", 2, 2, T, .5, name="CholDZ"),
mxAlgebra(CholDZ %*% t(CholDZ), name="expCovDZ"),
mxData(DataDZ, type="raw"),
mxFitFunctionML(),mxExpectationNormal("expCovDZ", "expMeanDZ", selVars)),
mxAlgebra(MZ.objective + DZ.objective, name="twin"),
mxFitFunctionAlgebra("twin"))
twinSatFit <- mxRun(twinSatModel, suppressWarnings=TRUE)
# Specify and Run Saturated Model with RawData and Matrix-style Input
# -----------------------------------------------------------------------
ExpMeanMZ <- mxEval(MZ.expMeanMZ, twinSatFit)
ExpCovMZ <- mxEval(MZ.expCovMZ, twinSatFit)
ExpMeanDZ <- mxEval(DZ.expMeanDZ, twinSatFit)
ExpCovDZ <- mxEval(DZ.expCovDZ, twinSatFit)
LL_Sat <- mxEval(objective, twinSatFit)
# Generate Saturated Model Output
# -----------------------------------------------------------------------
twinSatModelSub1 <- twinSatModel
twinSatModelSub1$MZ$expMeanMZ <- mxMatrix("Full", 1, 2, T, 0, "mMZ", name="expMeanMZ")
twinSatModelSub1$DZ$expMeanDZ <- mxMatrix("Full", 1, 2, T, 0, "mDZ", name="expMeanDZ")
twinSatFitSub1 <- mxRun(twinSatModelSub1, suppressWarnings=TRUE)
# Specify and Run Saturated SubModel 1 equating means across twin order
# -----------------------------------------------------------------------
twinSatModelSub2 <- twinSatModelSub1
twinSatModelSub2$MZ$expMeanMZ <- mxMatrix("Full", 1, 2, T, 0, "mean", name="expMeanMZ")
twinSatModelSub2$DZ$expMeanDZ <- mxMatrix("Full", 1, 2, T, 0, "mean", name="expMeanDZ")
twinSatFitSub2 <- mxRun(twinSatModelSub2, suppressWarnings=TRUE)
# Specify and Run Saturated SubModel 2 equating means across zygosity
# -----------------------------------------------------------------------
LL_Sat <- mxEval(objective, twinSatFit)
LL_Sub1 <- mxEval(objective, twinSatFitSub1)
LRT1 <- LL_Sub1 - LL_Sat
LL_Sub2 <- mxEval(objective, twinSatFitSub2)
LRT2 <- LL_Sub2 - LL_Sat
# Generate Saturated Model Comparison Output
# -----------------------------------------------------------------------
twinACEModel <- mxModel("twinACE",
mxMatrix("Full", 1, 2, T, 20, "mean", name="expMean"),
# Matrix expMean for expected mean
# vector for MZ and DZ twins
# -------------------------------------
mxMatrix("Full", nrow=1, ncol=1, free=TRUE, values=.6, label="a", name="X"),
mxMatrix("Full", nrow=1, ncol=1, free=TRUE, values=.6, label="c", name="Y"),
mxMatrix("Full", nrow=1, ncol=1, free=TRUE, values=.6, label="e", name="Z"),
# Matrices X, Y, and Z to store the
# a, c, and e path coefficients
# -------------------------------------
mxAlgebra(X * t(X), name="A"),
mxAlgebra(Y * t(Y), name="C"),
mxAlgebra(Z * t(Z), name="E"),
# Matrixes A, C, and E to compute
# A, C, and E variance components
# -------------------------------------
mxAlgebra(rbind(cbind(A+C+E , A+C),
cbind(A+C , A+C+E)), name="expCovMZ"),
# Matrix expCOVMZ for expected
# covariance matrix for MZ twins
# -------------------------------------
mxModel("MZ",
mxData(DataMZ, type="raw"),
mxFitFunctionML(),mxExpectationNormal("twinACE.expCovMZ", "twinACE.expMean",selVars)),
mxAlgebra(rbind(cbind(A+C+E , .5%x%A+C),
cbind(.5%x%A+C , A+C+E)), name="expCovDZ"),
# Matrix expCOVMZ for expected
# covariance matrix for DZ twins
# -------------------------------------
mxModel("DZ",
mxData(DataDZ, type="raw"),
mxFitFunctionML(),mxExpectationNormal("twinACE.expCovDZ", "twinACE.expMean",selVars)),
mxAlgebra(MZ.objective + DZ.objective, name="twin"),
mxFitFunctionAlgebra("twin"))
twinACEFit <- mxRun(twinACEModel, suppressWarnings=TRUE)
# Specify and Run ACE Model with RawData and Matrix-style Input
# -----------------------------------------------------------------------
LL_ACE <- mxEval(objective, twinACEFit)
LRT_ACE= LL_ACE - LL_Sat
MZc <- mxEval(expCovMZ, twinACEFit)
DZc <- mxEval(expCovDZ, twinACEFit)
M <- mxEval(expMean, twinACEFit)
# Retrieve expected mean vector and
# expected covariance matrices
# -------------------------------------
A <- mxEval(A, twinACEFit)
C <- mxEval(C, twinACEFit)
E <- mxEval(E, twinACEFit)
# Retrieve the A, C, and E
# variance components
# -------------------------------------
V <- (A+C+E)
a2 <- A/V
c2 <- C/V
e2 <- E/V
# Calculate standardized variance
# components
# -------------------------------------
ACEest <- rbind(cbind(A,C,E),cbind(a2,c2,e2))
ACEest <- data.frame(ACEest, row.names=c("Variance Components","Standardized VC"))
names(ACEest)<-c("A", "C", "E")
ACEest; LL_ACE; LRT_ACE
#Build and print reporting table with
# row and column names
# -------------------------------------
# Generate ACE Model Output
# -----------------------------------------------------------------------
twinAEModel <- twinACEModel
twinAEModel$twinACE$Y <- mxMatrix("Full", 1, 1, F, 0, "c", name="Y") # drop c
twinAEFit <- mxRun(twinAEModel, suppressWarnings=TRUE)
# Specify and Fit Reduced AE Model
# ----------------------------------------------------------------------
LL_AE <- mxEval(objective, twinAEFit)
MZc <- mxEval(expCovMZ, twinAEFit)
DZc <- mxEval(expCovDZ, twinAEFit)
M <- mxEval(expMean, twinAEFit)
# Retrieve expected mean vector and
# expected covariance matrices
# -------------------------------------
A <- mxEval(A, twinAEFit)
C <- mxEval(C, twinAEFit)
E <- mxEval(E, twinAEFit)
# Retrieve the A, C and E variance
# components
# -------------------------------------
V <- (A+C+E)
a2 <- A/V
c2 <- C/V
e2 <- E/V
# Calculate standardized variance
# components
# -------------------------------------
AEest <- rbind(cbind(A,C,E),cbind(a2,c2,e2))
AEest <- data.frame(ACEest, row.names=c("Variance Components","Standardized VC"))
names(ACEest)<-c("A", "C", "E")
AEest; LL_AE;
# Build and print reporting table with
# row and column names
# -------------------------------------
LRT_ACE_AE <- LL_AE - LL_ACE
LRT_ACE_AE
# Calculate and print likelihood ratio
# test
# -------------------------------------
# Generate ACE Model Output
# -----------------------------------------------------------------------
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