Hi,
I couldn't find any existing OpenMx codes to conduct bivariate genetic modelling for continuous and ordinal variables with covariates, so I've adapted Hermine Mae's twoACEvj.R code (bivariate ACE model for continuous and ordinal variables) by adding covariates to the code. I've done so by introducing separate regression coefficients for the continuous and ordinal variables. The code ran successfully, and the output seemed to be quite reasonable - the estimated ACE for the continuous variable was similar to the univariate ACE output, but the ordinal variable's estimated ACE was quite different: Bivariate's ACE output = (.61, 0, .39); Univariate ACE output = (.48, .11, .41).
If it helps, I have included a segment of my code with how I incorporated the covariates below. Any advice or comments will be greatly appreciated! Thanks!
# PREPARE MODEL # Matrix for moderating/interacting variable defSex <- mxMatrix( type="Full", nrow=1, ncol=2, free=FALSE, labels=c("data.Sex1","data.Sex2"), name="Sex") # Matrices declared to store linear Coefficients for covariate B_SexOrd <- mxMatrix( type="Full", nrow=nth, ncol=1, free=TRUE, values= .01, labels="betaSexOrd", name="bSexOrd") B_SexCon <- mxMatrix( type="Full", nrow=1, ncol=2, free=c(T,F), values= c(.01, 0), labels=c('bSexV1','bSexV2'), name="bSexCon") meanSexOrd <- mxAlgebra( bSexOrd%x%Sex, name="SexROrd") meanSexCon <- mxAlgebra( bSexCon%x%Sex, name="SexRCon") #age defAge <- mxMatrix( type="Full", nrow=1, ncol=2, free=FALSE, labels=c("data.Age1","data.Age2"), name="Age") # Matrices declared to store linear Coefficients for covariate B_AgeOrd <- mxMatrix( type="Full", nrow=nth, ncol=1, free=FALSE, values= 0, labels="betaAgeOrd", name="bAgeOrd") B_AgeCon <- mxMatrix( type="Full", nrow=1, ncol=2, free=c(T,F), values= c(.01,0), labels=c('bAgeV1','bAgeV2'), name="bAgeCon") meanAgeOrd <- mxAlgebra( bAgeOrd%x%Age, name="AgeROrd") meanAgeCon <- mxAlgebra( bAgeCon%x%Age, name="AgeRCon") #YrsEd defYEd <- mxMatrix( type="Full", nrow=1, ncol=2, free=FALSE, labels=c("data.yrsEd1","data.yrsEd2"), name="YEd") # Matrices declared to store linear Coefficients for covariate B_YEdOrd <- mxMatrix( type="Full", nrow=nth, ncol=1, free=FALSE, values= 0, labels="betaYEdOrd", name="bYEdOrd") B_YEdCon <- mxMatrix( type="Full", nrow=1, ncol=2, free=c(T,F), values= c(.01, 0), labels=c('bYEdV1','bYEdV2'), name="bYEdCon") meanYEdOrd <- mxAlgebra( bYEdOrd%x%YEd, name="YEdROrd") meanYEdCon <- mxAlgebra( bYEdCon%x%YEd, name="YEdRCon") #Age-related hearing condition defAHearing <- mxMatrix( type="Full", nrow=1, ncol=2, free=FALSE, labels=c("data.AHearing1","data.AHearing2"), name="AHearing") # Matrices declared to store linear Coefficients for covariate B_AHearingOrd <- mxMatrix( type="Full", nrow=nth, ncol=1, free=TRUE, values= .01, labels="betaAHearOrd", name="bAHearingOrd") B_AHearingCon <- mxMatrix( type="Full", nrow=1, ncol=2, free=c(T,F), values= c(.01, 0), labels=c('bAHearV1','bAHearV2'), name="bAHearingCon") meanAHearingOrd <- mxAlgebra( bAHearingOrd%x%AHearing, name="AHearingROrd") meanAHearingCon <- mxAlgebra( bAHearingCon%x%AHearing, name="AHearingRCon") #Bilateral hearing condition defBHearing <- mxMatrix( type="Full", nrow=1, ncol=2, free=FALSE, labels=c("data.BHearing1","data.BHearing2"), name="BHearing") # Matrices declared to store linear Coefficients for covariate B_BHearingOrd <- mxMatrix( type="Full", nrow=nth, ncol=1, free=FALSE, values= 0, labels="betaBHearOrd", name="bBHearingOrd") B_BHearingCon <- mxMatrix( type="Full", nrow=1, ncol=2, free=c(T,F), values= c(.01, 0), labels=c('bBHearV1','bBHearV2'), name="bBHearingCon") meanBHearingOrd <- mxAlgebra( bBHearingOrd%x%BHearing, name="BHearingROrd") meanBHearingCon <- mxAlgebra( bBHearingCon%x%BHearing, name="BHearingRCon") # Matrix & Algebra for expected means vector and expected thresholds intercept <- mxMatrix( type="Full", nrow=1, ncol=ntv, free=c(T,F), values=c(3,0), labels=c("meanP","binary"), name="intercept" ) threG <- mxMatrix( type="Full", nrow=nth, ncol=nv, free=TRUE, values=svTh, lbound=lbTh, labels=labThZ, name="Thre" ) inc <- mxMatrix( type="Lower", nrow=nth, ncol=nth, free=FALSE, values=1, name="Inc" ) threT <- mxAlgebra( expression= Inc %*% Thre, name="expThre" ) threC <- mxAlgebra( expression = expThre + AgeROrd + SexROrd + YEdROrd + AHearingROrd + BHearingROrd, name = "expThreC") #with covariates expMean <- mxAlgebra( intercept + AgeRCon + SexRCon + YEdRCon + AHearingRCon + BHearingRCon, name="expMean") inclusions <- list (defSex, B_SexOrd, B_SexCon, meanSexOrd, meanSexCon, defAge, B_AgeOrd, B_AgeCon, meanAgeOrd, meanAgeCon, defYEd, B_YEdOrd, B_YEdCon, meanYEdOrd, meanYEdCon, defAHearing, B_AHearingOrd, B_AHearingCon, meanAHearingOrd, meanAHearingCon, defBHearing, B_BHearingOrd, B_BHearingCon, meanBHearingOrd, meanBHearingCon, expMean, intercept, threG, threT, threC)
And the specification for expMZ and expDZ:
# Objective objects for Multiple Groups expMZ <- mxExpectationNormal( covariance="expCovMZ", means="expMean", dimnames=c('Vars1','PVars1','Vars2','PVars2'), thresholds="expThreC", threshnames=c('PVars1','PVars2') ) expDZ <- mxExpectationNormal( covariance="expCovDZ", means="expMean", dimnames=c('Vars1','PVars1','Vars2','PVars2'), thresholds="expThreC", threshnames=c('PVars1','PVars2') )