Intra Class Corelations

# Select Variables for Analysis
vars      <- "AG_Ln"                     # list of variables names
nv        <- 1                         # number of variables
ntv       <- nv*2                      # number of total variables
selVars   <- paste(vars,c(rep(1,nv),rep(2,nv)),sep="")
 
# Select Covariates for Analysis
#twinData[,'age'] <- twinData[,'age']/100
#twinData  <- twinData[-which(is.na(twinData$age)),]
covVars   <- c("age","Sex1","Sex2")
 
# Select Data for Analysis
mzData    <- subset(twinData, Zyg==1, c(selVars, covVars))
dzData    <- subset(twinData, Zyg==2, c(selVars, covVars))
 
# Set Starting Values
svMe      <- 4                       # start value for means
svPa      <- .4                        # start value for path coefficient
svPe      <- .8                        # start value for path coefficient for e
lbPa      <- .01                     # start value for lower bounds
 
# ------------------------------------------------------------------------------
# PREPARE MODEL
 
# ACE Model
# Create Matrices for Covariates and linear Regression Coefficients
defAge    <- mxMatrix( type="Full", nrow=1, ncol=1, free=FALSE, labels=c("data.age"), name="Age" )
pathB1     <- mxMatrix( type="Full", nrow=1, ncol=1, free=TRUE, values=.01, label="b11", name="b1" )
defSex    <- mxMatrix( type="Full", nrow=1, ncol=2, free=FALSE, labels=c("data.Sex1", "data.Sex2"), name="Sex" )
pathB2    <- mxMatrix( type="Full", nrow=1, ncol=1, free=TRUE, values=.01, label="b12", name="b2" )
 
# Create Algebra for expected Mean Matrices
meanG     <- mxMatrix( type="Full", nrow=1, ncol=ntv, free=TRUE, values=svMe, labels="xbmi", name="meanG" )
expMean   <- mxAlgebra( expression= meanG + cbind(b1%*%Age,b1%*%Age)+b2%*%Sex, name="expMean" )
 
# Create Matrices for Path Coefficients
pathA     <- mxMatrix( type="Lower", nrow=nv, ncol=nv, free=TRUE, values=svPa, label="a11", lbound=lbPa, name="a" ) 
pathC     <- mxMatrix( type="Lower", nrow=nv, ncol=nv, free=TRUE, values=svPa, label="c11", lbound=lbPa, name="c" )
pathE     <- mxMatrix( type="Lower", nrow=nv, ncol=nv, free=TRUE, values=svPe, label="e11", lbound=lbPa, name="e" )
 
# Create Algebra for Variance Components
covA      <- mxAlgebra( expression=a %*% t(a), name="A" )
covC      <- mxAlgebra( expression=c %*% t(c), name="C" ) 
covE      <- mxAlgebra( expression=e %*% t(e), name="E" )
 
# Create Algebra for expected Variance/Covariance Matrices in MZ & DZ twins
covP      <- mxAlgebra( expression= A+C+E, name="V" )
covMZ     <- mxAlgebra( expression= A+C, name="cMZ" )
covDZ     <- mxAlgebra( expression= 0.5%x%A+ C, name="cDZ" )
expCovMZ  <- mxAlgebra( expression= rbind( cbind(V, cMZ), cbind(t(cMZ), V)), name="expCovMZ" )
expCovDZ  <- mxAlgebra( expression= rbind( cbind(V, cDZ), cbind(t(cDZ), V)), name="expCovDZ" )
 
# Create Data Objects for Multiple Groups
dataMZ    <- mxData( observed=mzData, type="raw" )
dataDZ    <- mxData( observed=dzData, type="raw" )
 
# Create Expectation Objects for Multiple Groups
expMZ     <- mxExpectationNormal( covariance="expCovMZ", means="expMean", dimnames=selVars )
expDZ     <- mxExpectationNormal( covariance="expCovDZ", means="expMean", dimnames=selVars )
funML     <- mxFitFunctionML()
 
# Create Model Objects for Multiple Groups
pars      <- list(pathB1,pathB2, meanG, pathA, pathC, pathE, covA, covC, covE, covP)
defs      <- list(defAge, defSex)
modelMZ   <- mxModel( name="MZ", pars, defs, expMean, covMZ, expCovMZ, dataMZ, expMZ, funML )
modelDZ   <- mxModel( name="DZ", pars, defs, expMean, covDZ, expCovDZ, dataDZ, expDZ, funML )
multi     <- mxFitFunctionMultigroup( c("MZ","DZ") )
 
# Create Algebra for Variance Components
rowVC     <- rep('VC',nv)
colVC     <- rep(c('A','C','E','SA','SC','SE'),each=nv)
estVC     <- mxAlgebra( expression=cbind(A,C,E,A/V,C/V,E/V), name="VC", dimnames=list(rowVC,colVC))
 
# Create Confidence Interval Objects
ciACE     <- mxCI( "VC" )
 
# Build Model with Confidence Intervals
modelACE  <- mxModel( "oneACEca", pars, modelMZ, modelDZ, multi, estVC, ciACE )
 
# ------------------------------------------------------------------------------
# RUN MODEL
 
# Run ACE Model
fitACE    <- mxTryHard( modelACE, intervals=T, extraTries = 10, finetuneGradient = T, exhaustive = T )
sumACE    <- summary( fitACE )
summary(fitACE)
# Compare with Saturated Model
mxCompare( fit, fitACE )
#lrtSAT(fitACE,-2ll,df)
 
# Print Goodness-of-fit Statistics & Parameter Estimates
fitGofs(fitACE)
fitEsts(fitACE)
 
# ------------------------------------------------------------------------------
# RUN SUBMODELS
 
# Test Significance of Covariate
modelCov  <- mxModel( fitACE, name="testCov" )
modelCov  <- omxSetParameters( modelCov, label=c("b11","b12"), free=FALSE, values=0 )
fitCov    <- mxRun( modelCov )
mxCompare( fitACE, fitCov )
 
# Run AE model
modelAE   <- mxModel( fitACE, name="oneAEca" )
modelAE   <- omxSetParameters( modelAE, labels="c11", free=FALSE, values=0 )
fitAE     <- mxRun( modelAE, intervals=T )
mxCompare( fitACE, fitAE )
fitGofs(fitAE)
fitEsts(fitAE)
summary(fitAE)
# Run CE model
modelCE   <- mxModel( fitACE, name="oneCEca" )
modelCE   <- omxSetParameters( modelCE, labels="a11", free=FALSE, values=0 )
fitCE     <- mxRun( modelCE, intervals=T )
mxCompare( fitACE, fitCE )
fitGofs(fitCE)
fitEsts(fitCE)
 
# Run E model
modelE    <- mxModel( fitAE, name="oneEca" )
modelE    <- omxSetParameters( modelE, labels="a11", free=FALSE, values=0 )
fitE      <- mxRun( modelE, intervals=T )
mxCompare( fitAE, fitE )
fitGofs(fitE)
fitEsts(fitE)
 
# Print Comparative Fit Statistics
mxCompare( fitACE, nested <- list(fitCov, fitAE, fitCE, fitE) )
round(rbind(fitACE$VC$result,fitAE$VC$result,fitCE$VC$result,fitE$VC$result),4)