1

Twin Analysis 103October 2010

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Specifications Continuous

mxMatrix mxAlgebra

CholMZ T1 T2 expCovMZ T1 T2

T1 #1 0 T1 var1 cov

T2 #2 #3 T2 cov var2

T1 T2

expMeanMZ

#4 #5

mzData selVars

fam bmi1 bmi2

1457 20 NA

1782 25 24

mxObjective

covariance=expCovMZ

means=expMeanMZ

dimnames=selVars

mxData observed=

mzData

type=raw

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MZ & DZ Twins Reared Together

MZ twins DZ twins

4 parameters

4

-2LL df Chi2* df p AIC Chi2# df p

Sat 4055.9176

7

ADE 4063.4177

37.52 6 0.28

517.4

AE 4067.6177

311.73 7 0.11

519.6

1

ACE 4067.6177

311.73 6 0.07

521.6

CE 4220.3177

4164.3

77 0

672.3

152.6 1 0

E 4591.7177

5535.8

68 0

1041.7

524.1 2 0

Goodness-of-Fit

Chi2*: likelihood ratio test compared to saturated model

Chi2#: likelihood ratio test compared to ADE or ACE model

5

a c e d a2 c2 e2 d2

Sat

ADE 0.57 0.41 0.54 0.32 0.17 0.29

AE 0.79 0.42 0.62 0.17

ACE 0.79 0 0.42 0.62 0 0.17

CE 0.68 0.56 0.46 0.32

E 0.88 0.78

Parameter Estimates

a2 , c2 etc. should be unstandardized variance components

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Specifications Binary

mxMatrix mxAlgebra

expCorMZ T1 T2

T1 1 0

T2 #2 1

T1 T2

expMeanMZ

0 0

expThreMZ

#4 #5mzDataBi

nselVars

fam ob1 ob2

1457 0 NA

1782 1 1mxObjective

covariance=expCorMZ

means=expMeanMZ

dimnames=selVars

thresholds=expThreMZ

mxData observed=

mzDataBin

type=raw

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Changes to OpenMx Code

mzDataBin[,1:2] <- mxFactor(mzDataBin[,1:2], levels = c(0:1))

# Constraint on variance of ordinal variablesmxConstraint( V== I, name="Var1"),

# Matrix & Algebra for expected means vectormxMatrix( "Zero", 1, ntv, name="expMeanMZ" ),

# Matrix & Algebra for expected thresholds# Binary

mxMatrix( "Full", 1, nv, free=TRUE, values=.8, label="thre", name="Thre" ),mxAlgebra( cbind(Th,Th), dimnames=list('th1',selVars), name="expThre" ),

# Ordinal mxMatrix( "Full", nth, ntv, free=T, values=thValues, lbound=thLBound, name="Thre"), mxMatrix( "Lower", nth, nth, free=FALSE, values=1, name="Inc" ), mxAlgebra( expression= Inc %*% Thre, name="ThreInc"), mxAlgebra( cbind(ThreInc,ThreInc),dimnames=list(thRows,selVars),name="expThreMZ" ),# Objective mxFIMLObjective( "ACE.expCovMZ", "ACE.expMean", selVars, thresholds="ACE.expThre" )

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-2LL df Chi2* df p AIC Chi2# df p

Sat

ADE 3

AE 4 1

ACE 3

CE 4 1

E 5 2

Goodness-of-Fit

Chi2*: likelihood ratio test compared to saturated model

Chi2#: likelihood ratio test compared to ADE or ACE model

9

a c e d a2 c2 e2 d2

Sat

ADE

AE

ACE

CE

E

Parameter Estimates

a2 , c2 etc. should be unstandardized variance components

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Specifications Ordinal

mxMatrix mxAlgebra

expCorMZ T1 T2expThreM

Zth1t1 th1t2

T1 1 0 th2t1 th2t2

T2 #2 1 th3t1 th3t2

T1 T2 Inc 1 0 0

expMeanMZ

0 0 1 1 0

Thre #4 #5 1 1 1

#6 #7

#8 #9

mzDataOrd

selVars

fam ob1 ob2

1457 0 NA

1782 1 1mxObjective

covariance=expCorMZ

means=expMeanMZ

dimnames=selVars

thresholds=expThreMZ

mxData observed=

mzDataOrd

type=raw

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Heterogeneity

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•Univariate Analysis: What are the contributions of additive genetic, dominance/shared environmental and unique environmental factors to the variance?

•Are the contributions of genetic and environmental factors equal for different groups, such as sex, race, ethnicity, SES, environmental exposure, etc.?

Heterogeneity Questions I

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•Are these differences due to differences in the magnitude of the effects (quantitative)?

• e.g. Is the contribution of genetic/environmental factors greater/smaller in males than in females?

•Are the differences due to differences in the nature of the effects (qualitative)?

• e.g. Are there different genetic/environmental factors influencing the trait in males and females?

Heterogeneity Questions II

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ComparisonConcordant for

group membershipDiscordant for

group membership

genderMZ & DZ:

MM & FF pairsDZ:

opposite sex pairs

ageMZ & DZ:

young & old pairs

nationalityMZ & DZ:

OZ & US pairs

environmentMZ & DZ:

urban & rural pairsMZ & DZ:

urban/ rural pairs

Groups

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Heterogeneity Modelsame sex pairs

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Homogeneity Modelsame sex pairs

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OS G1 G2 EP

Heterogeneity 12 a1 c1 e1 a2 c2 e2 6

Homogeneity 12 a1 c1 e1 a1 c1 e1 3

Models for Concordant Pairs

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Heterogeneity Twin Analysis

HetTwinQnMaRawCon.R

# Prepare Data and Print Summary Statistics# -----------------------------------------------------------------------data(twinData)summary(twinData)Vars <- 'bmi'nv <- 1selVars <- paste(Vars,c(rep(1,nv),rep(2,nv)),sep="") ntv <- nv*2mzfData <- subset(twinData, zyg==1, selVars)dzfData <- subset(twinData, zyg==3, selVars)mzmData <- subset(twinData, zyg==2, selVars)dzmData <- subset(twinData, zyg==4, selVars)

colMeans(mzfData,na.rm=TRUE)....cov(mzfData,use="complete")....

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ACE males/ femalesHetTwinQnMaRawCon.R

# Fit Heterogeneity ACE Model with RawData and Matrices Input# -----------------------------------------------------------------------univHetACEModel <- mxModel("univHetACE",

mxModel("ACE",# Matrices a, c, and e to store a, c, and e path coefficients

mxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="am11", name="am" ),mxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="cm11", name="cm" ),mxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="em11", name="em" ),mxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="af11", name="af" ),mxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="cf11", name="cf" ),mxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="ef11", name="ef" ),

# Matrices A, C, and E compute variance componentsmxAlgebra( am %*% t(am), name="Am" ),mxAlgebra( cm %*% t(cm), name="Cm" ),mxAlgebra( em %*% t(em), name="Em" ),mxAlgebra( am %*% t(am), name="Af" ),mxAlgebra( cm %*% t(cm), name="Cf" ),mxAlgebra( em %*% t(em), name="Ef" ),

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inverse Standard Deviations

HetTwinQnMaRawCon.R

# Algebra to compute total variances and standard deviations (diagonal only)mxAlgebra( Am+Cm+Em, name="Vm" ),mxAlgebra( Af+Cf+Ef, name="Vf" ),mxMatrix( "Iden", nv, nv, name="I"),mxAlgebra( solve(sqrt(I*Vm)), name="isdm"),mxAlgebra( solve(sqrt(I*Vf)), name="isdf"),

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5 expected Cov MatricesHetTwinQnMaRawCon.R

# Matrix & Algebra for expected means vectormxMatrix( "Full", 1, nv, free=TRUE, values= 20, label="mean", name="M" ),mxAlgebra( cbind(M,M), name="expMean"),

# Algebra for expected variance/covariance matrix in MZmxAlgebra( rbind ( cbind(Am+Cm+Em , Am+Cm),

cbind(Am+Cm , Am+Cm+Em)), name="expCovMZm" ), mxAlgebra( rbind ( cbind(Af+Cf+Ef , Af+Cf),

cbind(Af+Cf , Af+Cf+Ef)), name="expCovMZf" ),# Algebra for expected variance/covariance matrix in DZ; 0.5, converted to 1*1 matrix

mxAlgebra( rbind ( cbind(Am+Cm+Em , 0.5%x%Am+Cm),cbind(0.5%x%Am+Cm , Am+Cm+Em)), name="expCovDZm" ),

mxAlgebra( rbind ( cbind(Af+Cf+Ef , 0.5%x%Af+Cf),cbind(0.5%x%Af+Cf , Af+Cf+Ef)), name="expCovDZf" )

),

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5 Data GroupsHetTwinQnMaRawCon.R

mxModel("MZm",mxData( observed=mzmData, "raw" ),mxFIMLObjective( ="ACE.expCovMZm", "ACE.expMean", selVars ) ),

mxModel("DZm", mxData( observed=dzmData, "raw" ),mxFIMLObjective( "ACE.expCovDZm", "ACE.expMean", selVars ) ),

mxModel("MZf",mxData( observed=mzfData, "raw" ),mxFIMLObjective( "ACE.expCovMZf", "ACE.expMean", selVars ) ),

mxModel("DZf", mxData( observed=dzfData, "raw" ),mxFIMLObjective( "ACE.expCovDZf", "ACE.expMean", selVars ) ),

mxAlgebra( MZm.objective + DZm.objective + MZf.objective + DZf.objective,name="-2sumll" ),

mxAlgebraObjective("-2sumll"))

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Estimates male|female

HetTwinQnMaRawCon.R

univHetACEFit <- mxRun(univHetACEModel)univHetACESumm <- summary(univHetACEFit)

# Generate Heterogeneity ACE Output# -----------------------------------------------------------------------parameterSpecifications(univHetACEFit)expectedMeansCovariances(univHetACEFit)tableFitStatistics(univHetACEFit)

# Generate Table of Parameter Estimates using mxEvalpathEstimatesACE <- round(mxEval(cbind(ACE.am,ACE.cm,ACE.em,ACE.af,ACE.cf,ACE.ef), univHetACEFit),4)varComponentsACE <- round(mxEval(cbind(ACE.Am/ACE.Vm,ACE.Cm/ACE.Vm, ACE.Em/ACE.Vm,ACE.Af/ACE.Vf,ACE.Cf/ACE.Vf,ACE.Ef/ACE.Vf), univHetACEFit),4)

rownames(pathEstimatesACE) <- 'pathEstimates'colnames(pathEstimatesACE) <- c('am','cm','em','af','cf','ef')rownames(varComponentsACE) <- 'varComponents'colnames(varComponentsACE) <- c('am^2','cm^2','em^2','af^2','cf^2','ef^2')

pathEstimatesACE; varComponentsACE

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Automated OutputHetTwinQnMaRawCon.R

# Generate List of Parameter Estimates and Derived Quantities using formatOutputMatricesACEpathMatricesM <- c("ACE.am","ACE.cm","ACE.em", "ACE.isdm","ACE.isdm %*% ACE.am","ACE.isdm %*% ACE.cm","ACE.isdm %*% ACE.em")ACEpathLabelsM <- c("pathEst_am","pathEst_cm","pathEst_em", "sdm","stPathEst_am","stPathEst_cm","stPathEst_em")ACEpathMatricesF <- c("ACE.af",....)ACEpathLabelsF <- c("pathEst_af",....)formatOutputMatrices(univHetACEFit,ACEpathMatricesM,ACEpathLabelsM,4)formatOutputMatrices(univHetACEFit,ACEpathMatricesF,ACEpathLabelsF,4)

ACEcovMatricesM <- c("ACE.Am","ACE.Cm","ACE.Em", "ACE.Vm","ACE.Am/ACE.Vm","ACE.Cm/ACE.Vm","ACE.Em/ACE.Vm")ACEcovLabelsM <- c("covComp_Am","covComp_Cm","covComp_Em", "Varm","stCovComp_Am","stCovComp_Cm","stCovComp_Em")ACEcovMatricesF <- c("ACE.Af",....)ACEcovLabelsF <- c("covComp_Af",....)formatOutputMatrices(univHetACEFit,ACEcovMatricesM,ACEcovLabelsM,4)formatOutputMatrices(univHetACEFit,ACEcovMatricesF,ACEcovLabelsF,4)

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Equate Labels 2 constrainHetTwinQnMaRawCon.R

# Fit Homogeneity ACE Model with RawData and Matrices Input# -----------------------------------------------------------------------univHomACEModel <- mxModel(univHetACEFit, name="univHomACE",

mxModel(univHetACEFit$ACE,mxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="a11", name="am" ),mxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="c11", name="cm" ),mxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="e11", name="em" ),mxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="a11", name="af" ),mxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="c11", name="cf" ),mxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="e11", name="ef" ) )

)univHomACEFit <- mxRun(univHomACEModel)univHomACESumm <- summary(univHomACEFit)

# Generate Homogeneity ACE Output# -----------------------------------------------------------------------parameterSpecifications(univHomACEFit)expectedMeansCovariances(univHomACEFit)tableFitStatistics(univHomACEFit)2

5

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Homogeneity Twin Analysis

HetTwinQnMaRawCon.R

# Generate Table of Parameter Estimates using mxEvalpathEstimatesACE <- round(mxEval(cbind(ACE.am,ACE.cm,ACE.em), univHomACEFit),4)varComponentsACE <- round(mxEval(cbind(ACE.Am/ACE.Vm,ACE.Cm/ACE.Vm, ACE.Em/ACE.Vm), univHomACEFit),4)

rownames(pathEstimatesACE) <- 'pathEstimates'colnames(pathEstimatesACE) <- c('a','c','e')rownames(varComponentsACE) <- 'varComponents'colnames(varComponentsACE) <- c('a^2','c^2','e^2')

pathEstimatesACEvarComponentsACE

# Generate List of Parameter Estimates and Derived Quantities using formatOutputMatricesformatOutputMatrices(univHomACEFit,ACEpathMatricesM,ACEpathLabelsM,4)formatOutputMatrices(univHomACEFit,ACEcovMatricesM,ACEcovLabelsM,4)

# Print Comparative Fit Statistics# -----------------------------------------------------------------------tableFitStatistics(univHetACEFit, univHomACEFit)

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General Modelsame & opposite sex pairs

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OS G1 G2 EP

Heterogeneity 15 a1 c1 e1 a2 c2 e2 6

Homogeneity 15 a1 c1 e1 a1 c1 e1 3

General I II

1515

a1 c1 e1

a1 c1 e1

a2 c2 e2 rg

a2 c2 e2 rc

77

Models for Concordant and Discordant Pairs

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•Homogeneity Model:

• no quantitative, no qualitative differences

•Heterogeneity Model:

• quantitative but no qualitative differences

•General Model:

• quantitative and qualitative differences

Summary of Models

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Moderated Model

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Moderated Twin AnalysisModTwinMaRawCon.R

# Prepare Data# -----------------------------------------------------------------------data(twinData)summary(twinData)oneVars <- 'bmi'nv <- 1selVars <- paste(Vars,c(rep(1,nv),rep(2,nv)),sep="") ntv <- nv*2twinData[,'age'] <- twinData[,'age']/100mzData <- as.data.frame(subset(twinData, zyg==7, c(bmi1,bmi2,age)))dzData <- as.data.frame(subset(twinData, zyg==9, c(bmi1,bmi2,age))) colMeans(mzData,na.rm=TRUE)colMeans(dzData,na.rm=TRUE)cov(mzData,use="complete")cov(dzData,use="complete")

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Moderated Means - bModTwinMaRawCon.R

# Fit Moderated ACE Model + Linear & Quadratic Moderated Means# -----------------------------------------------------------------------univModMeanslqACEModel <- mxModel("univModMeanslqACE",

mxModel("ACE",# Matrices a, c, and e to store a, c, and e path coefficients

mxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="a11", name="a" ),mxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="c11", name="c" ),mxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="e11", name="e" ),

# Matrices a, c, and e to store moderated a, c, and e path coefficientsmxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="aI11", name="aI" ),mxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="cI11", name="cI" ),mxMatrix( "Full", nv, nv, free=TRUE, values=.6, label="eI11", name="eI" ),

# Matrix & Algebra for expected means vectormxMatrix( "Full", 1, nv, free=TRUE, values= 20, label="mean", name="M" ),mxMatrix( "Full", 1, 2, free=TRUE, values=.01, label=c("l11","q11"), name="b" ),

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Moderated VarComponents

ModTwinMaRawCon.R

# Matrices A, C, and E compute non-moderated variance components mxAlgebra( a %*% t(a), name="A" ),mxAlgebra( c %*% t(c), name="C" ),mxAlgebra( e %*% t(e), name="E" ),

# Algebra to compute total variances and inverse of standard deviations (diagonal only)mxAlgebra( A+C+E, name="V" ),mxMatrix( "Iden", nv, nv, name="I"),mxAlgebra( solve(sqrt(I*V)), name="isd"),

# Matrices & Algebra to plot means by agemxMatrix( "Full", 5, 1, values=c(.3,.4,.5,.6,.7), name="Ages"),mxMatrix( "Full", 2, 5, values=c(.3,.09,.4,.16,.5,.25,.6,.36,.7,.49), name="Agelq"),mxMatrix( "Unit", 5, 1, name="u"),mxAlgebra( unit%x%M+ t(b%*%Agelq), name="MI"),mxAlgebra( diag2vec((u%x%a+ Ages%x%aI) %*% t(u%x%a+ Ages%x%aI)), name="AI" ),mxAlgebra( diag2vec((u%x%c+ Ages%x%cI) %*% t(u%x%c+ Ages%*%cI)), name="CI" ),mxAlgebra( diag2vec((u%x%e+ Ages%x%eI) %*% t(u%x%e+ Ages%*%eI)), name="EI" ),mxAlgebra( AI+CI+EI, name="VI" ),mxAlgebra( cbind(MI,AI,CI,EI,VI), name="estByAge" ),mxAlgebra( cbind(MI,AI/VI,CI/VI,EI/VI,VI), name="stEstByAge" ) ),

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Algebra in MZ modelModTwinMaRawCon.R

mxModel("MZ",# Matrix for moderating/interacting variable

mxMatrix( "Full", 1, 1, free=FALSE, labels=c("data.age"), name="Age"), # Matrices A, C, and E compute variance components

mxAlgebra( (ACE.a+ Age%*%ACE.aI) %*% t(ACE.a+ Age%*%ACE.aI), name="A" ),mxAlgebra( (ACE.c+ Age%*%ACE.cI) %*% t(ACE.c+ Age%*%ACE.cI), name="C" ),mxAlgebra( (ACE.e+ Age%*%ACE.eI) %*% t(ACE.e+ Age%*%ACE.eI), name="E" ),

# Algebra for expected variance/covariance matrix and expected mean vector in MZmxAlgebra( rbind ( cbind(A+C+E , A+C),

cbind(A+C , A+C+E)), name="expCovMZ" ),mxAlgebra( ACE.b%*%rbind(Age,Age^2), name="AgeR"),mxAlgebra( cbind((ACE.M + AgeR),(ACE.M + AgeR)), name="expMean"),

# Data & ObjectivemxData( observed=mzData, "raw" ),mxFIMLObjective( "expCovMZ", "expMean", selVars )

),

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Definition VariableModTwinMaRawCon.R

mxModel("DZ", mxMatrix( "Full", 1, 1, free=FALSE, labels=c("data.age"), name="Age"),

# Matrices A, C, and E compute variance componentsmxAlgebra( (ACE.a+Age%*%ACE.aI) %*% t(ACE.a+Age%*%ACE.aI), name="A" ),mxAlgebra( (ACE.c+Age%*%ACE.cI) %*% t(ACE.c+Age%*%ACE.cI), name="C" ),mxAlgebra( (ACE.e+Age%*%ACE.eI) %*% t(ACE.e+Age%*%ACE.eI), name="E" ),

# Algebra for expected variance/covariance matrix in DZmxAlgebra( rbind ( cbind(A+C+E , 0.5%x%A+C),

cbind(0.5%x%A+C , A+C+E)), name="expCovDZ" ),mxAlgebra( ACE.b%*%rbind(Age,Age^2), name="AgeR"),mxAlgebra( cbind((ACE.M + AgeR),(ACE.M + AgeR)), name="expMean"),

# Data & ObjectivemxData( observed=dzData, "raw" ),mxFIMLObjective( "expCovDZ", "expMean", selVars )

),mxAlgebra( MZ.objective + DZ.objective, name="minus2sumloglikelihood" ),mxAlgebraObjective("-2sumll"))

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Estimated ace|moderated

ModTwinMaRawCon.R

univModMeanslqACEFit <- mxRun(univModMeanslqACEModel)univModMeanslqACESumm <- summary(univModMeanslqACEFit)

# Generate Moderated ACE Output# -----------------------------------------------------------------------parameterSpecifications(univModMeanslqACEFit)expectedMeansCovariances(univModMeanslqACEFit)tableFitStatistics(univModMeanslqACEFit)

# Generate Table of Parameter Estimates using mxEvalpathEstimatesACE <- round( mxEval(cbind(ACE.a,ACE.c,ACE.e,ACE.aI,ACE.cI,ACE.eI), univModMeanslqACEFit),4)varComponentsACE <- round( mxEval(cbind(ACE.A/ACE.V,ACE.C/ACE.V,ACE.E/ACE.V), univModMeanslqACEFit),4)rownames(pathEstimatesACE) <- 'pathEstimates'colnames(pathEstimatesACE) <- c('a','c','e','aI','cI','eI')rownames(varComponentsACE) <- 'varComponents'colnames(varComponentsACE) <- c('a^2','c^2','e^2')pathEstimatesACE; varComponentsACE

36

37

AutomatedModTwinMaRawCon.R

# Generate List of Parameter Estimates and Derived Quantities using formatOutputMatricesACEpathMatrices <- c("ACE.a","ACE.c","ACE.e", "ACE.isd","ACE.isd %*% ACE.a","ACE.isd %*% ACE.c","ACE.isd %*% ACE.e")ACEpathLabels <- c("pathEst_a","pathEst_c","pathEst_e", "sd","stParEst_a","stPathEst_c","stPathEst_e")formatOutputMatrices(univModMeanslqACEFit,ACEpathMatrices,ACEpathLabels,4)

ACEpathMatricesI <- c("ACE.aI","ACE.cI","ACE.eI","ACE.isdI")ACEpathLabelsI <- c("pathEst_aI","pathEst_cI","pathEst_eI")formatOutputMatrices(univModMeanslqACEFit,ACEpathMatricesI,ACEpathLabelsI,4)ACEcovMatrices <- c("ACE.A","ACE.C","ACE.E", "ACE.V","ACE.A/ACE.V","ACE.C/ACE.V","ACE.E/ACE.V")ACEcovLabels <- c("covComp_A","covComp_C","covComp_E", "Var","stCovComp_A","stCovComp_C","stCovComp_E")formatOutputMatrices(univModMeanslqACEFit,ACEcovMatrices,ACEcovLabels,4)

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Quantities by AgeModTwinMaRawCon.R

# Generate Quantities by AgeestByAge <- mxEval(ACE.estByAge,univModMeanslqACEFit)stEstByAge <- mxEval(ACE.stEstByAge,univModMeanslqACEFit)

rowsEstByAge <- c("Age30","Age40","Age50","Age60","Age70")colsEstByAge <- c("MI","AI","CI","EI","VI")formatMatrix(estByAge,list(rowsEstByAge,colsEstByAge),4)formatMatrix(stEstByAge,list(rowsEstByAge,colsEstByAge),4)

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LinearQuadratic Regression

ModTwinMaRawCon.R

# Fit Moderated ACE model + Linear Moderated Means# -----------------------------------------------------------------------univModMeanslACEModel <- mxModel(univModMeanslqACEFit, name="univModMeanslACE",

mxModel(univModMeanslqACEFit$ACE,mxMatrix( "Full", 1, 2, free=c(T,F), values=c(.01,0), label=c("l11","q11"), name="b" )

))univModMeanslACEFit <- mxRun(univModMeanslACEModel)

# Fit Moderated ACE model + no Moderated Means# -----------------------------------------------------------------------univModACEModel <- mxModel(univModMeanslACEFit, name="univModACE",

mxModel(univModMeanslACEFit$ACE,mxMatrix( "Full", 1, 2, free=F, values=0, label=c("l11","q11"), name="b" )

))univModACEFit <- mxRun(univModACEModel)

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UnModeratedModTwinMaRawCon.R

# Fit non-Moderated ACE model# -----------------------------------------------------------------------univUnModACEModel <- mxModel(univModACEFit, name="univUnModACE",

mxModel(univModACEFit$ACE,mxMatrix( "Full", 1, 1, free=F, values=0, label="aI11", name="aI" ),mxMatrix( "Full", 1, 1, free=F, values=0, label="cI11", name="cI" ),

mxMatrix( "Full", 1, 1, free=F, values=0, label="eI11", name="eI" ))

)univUnModACEFit <- mxRun(univUnModACEModel)univUnModACESumm <- summary(univUnModACEFit)

# Generate UnModerated ACE Output# -----------------------------------------------------------------------parameterSpecifications(univUnModACEFit)expectedMeansCovariances(univUnModACEFit)

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Fit StatisticsModTwinMaRawCon.R

# Generate Table of Parameter Estimates using mxEvalpathEstimatesACE <- round( mxEval(cbind(ACE.a,ACE.c,ACE.e,ACE.aI,ACE.cI,ACE.eI), univUnModACEFit),4)varComponentsACE <- round( mxEval(cbind(ACE.A/ACE.V,ACE.C/ACE.V,ACE.E/ACE.V), univUnModACEFit),4)rownames(pathEstimatesACE) <- 'pathEstimates'colnames(pathEstimatesACE) <- c('a','c','e','aI','cI','eI')rownames(varComponentsACE) <- 'varComponents'colnames(varComponentsACE) <- c('a^2','c^2','e^2','aI^2','cI^2','eI^2')pathEstimatesACEvarComponentsACE

# Print Comparative Fit Statistics# -----------------------------------------------------------------------univModACENested <- c(univModMeanslACEFit,univModACEFit,univUnModACEFit)tableFitStatistics(univModMeanslqACEFit,univModACENested)tableFitStatistics(univModACEFit, univUnModACEFit)