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Multivariate ACE-ADE model

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JuanJMV's picture
Joined: 07/20/2016 - 13:13
Multivariate ACE-ADE model


I am trying to fit a 5-variate model. But I am not sure about the best way to do it.

I have got these results from the univariate analyses

ADE 0.34 0.10 0.57
AE 0.42 * 0.58

ADE 0.26 0.16 0.58
AE 0.41 * 0.59

ACE 0.29 0.13 0.58
AE 0.45 * 0.55
CE * 0.33 0.67

ADE 0.23 0.17 0.59
AE 0.39 * 0.61

ACE 0.35 0.05 0.60
AE 0.41 * 0.59
CE * 0.29 0.71

Therefore, I have:
AE model for Variable 1
AE model for Variable 2
ACE model for Variable 3
ADE model for Variable 4
AE model for Variable 5

I have fitted several models but I am not sure what model should I select.
5-ACE model: BIC= -310035.618; AIC=-10692.932
5-ADE model BIC= -310065.74; AIC=--10723.10
5-AE model BIC= -310144.380; AIC= -10703.607
*The comparison between ACE and AE Is non-significant therefore I can select the AE model but the comparison between ADE and AE is significant therefore I cannot select the nested model

I have also tried to fit a 5variables-ACE-ADE model (BIC=-310104.987; AIC=-10696.909) with (C for variables 3 and 5 and D for variables 1,2 and 4).

However, I am not sure if I adapted it correctly since I am getting much lower values for C (near 0) and D in comparison with the univariate results or 5-ACE or ADE models.

*The comparison between ADCE and AE is non-significant.

Here is my adapted script.

# Select Variables for Analysis
vars      <- c('VAR1','VAR2','VAR3','VAR4', "VAR5" )              # list of variables names
nv        <- 5                         # 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
covVars   <- c('age', "Sex1" , "Sex2")
nc        <- 3                         # number of covariates
ordData <- twinData
# Select Data for Analysis
mzData    <- subset(ordData, Zyg==1| Zyg==3, c(selVars, covVars))
dzData    <- subset(ordData, Zyg==2 | Zyg==4| Zyg==5, c(selVars, covVars))
# Set Starting Values 
svMe      <- c(1.2,1.1,1.1, 1.2,1.2)                   # start value for means
svPa      <- .4                        # start value for path coefficient
svPaD     <- vech(diag(svPa,nv,nv))    # start values for diagonal of covariance matrix
svPe      <- .8                        # start value for path coefficient for e
svPeD     <- vech(diag(svPe,nv,nv))    # start values for diagonal of covariance matrix
lbPa      <- .0001                     # start value for lower bounds
lbPaD     <- diag(lbPa,nv,nv)          # lower bounds for diagonal of covariance matrix
lbPaD[lower.tri(lbPaD)] <- -10         # lower bounds for below diagonal elements
lbPaD[upper.tri(lbPaD)] <- NA          # lower bounds for above diagonal elements
# Create Labels
labMe     <- paste("mean",vars,sep="_")
labBe     <- labFull("beta",nc,1)
# ------------------------------------------------------------------------------
# ADCE Model
defAge    <- mxMatrix( type="Full", nrow=1, ncol=1, free=FALSE, labels=c("data.age"), name="Age" )
pathB1     <- mxMatrix( type="Full", nrow=5, ncol=1, free=TRUE, values=.01, label=c("b11","b12", "b13","b14","b15"), name="b1" )
defSex    <- mxMatrix( type="Full", nrow=1, ncol=10, free=FALSE, labels=c("data.Sex1", "data.Sex1", "data.Sex1", "data.Sex1","data.Sex1", "data.Sex2","data.Sex2","data.Sex2", "data.Sex2", "data.Sex2"), name="Sex" )
pathB2     <- mxMatrix( type="Full", nrow=1, ncol=10, free=TRUE, values=.01, label=c("b21", "b22","b23","b24","b25", "b21", "b22", "b23","b24","b25"), name="b2" )
# Create Algebra for expected Mean Matrices
meanG     <- mxMatrix( type="Full", nrow=1, ncol=ntv, free=TRUE, values=svMe, labels=labMe, name="meanG" )
expMean   <- mxAlgebra( expression= meanG + cbind(t(b1%*%Age),t(b1%*%Age))+b2*Sex, name="expMean" )
# Create Matrices for Path Coefficients
pathA     <- mxMatrix( type="Lower", nrow=nv, ncol=nv, free=TRUE, values=svPaD, label=labLower("a",nv), lbound=lbPaD, name="a" ) 
pathC     <- mxMatrix( type="Full", nrow=nv, ncol=nv, free=c(F,F,T,F,T), values=c(0,0,0.3,0,0.3), label=c(NA,NA,"c11",NA,"c22"),  name="c" )
pathD     <- mxMatrix( type="Full", nrow=nv, ncol=nv, free=c(T,T,F,T,F), values=c(0.3,0.3,0,0.3,0), label=c("d11","d22",NA,"d33",NA), name="d" )
pathE     <- mxMatrix( type="Lower", nrow=nv, ncol=nv, free=TRUE, values=svPeD, label=labLower("e",nv), lbound=lbPaD, name="e" )
# Create Algebra for Variance Comptwonts
covA      <- mxAlgebra( expression=a %*% t(a), name="A" )
covC      <- mxAlgebra( expression=c %*% t(c), name="C" ) 
covD      <- mxAlgebra( expression=d %*% t(d), name="D" ) 
covE      <- mxAlgebra( expression=e %*% t(e), name="E" )
# Create Algebra for expected Variance/Covariance Matrices in MZ & DZ twins
covP      <- mxAlgebra( expression=A+C+D+E, name="V" )
covMZ     <- mxAlgebra( expression= A+C+D, name="cMZ" )
covDZ     <- mxAlgebra( expression= 0.5%x%A+C+0.25%x%D, 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 Algebra for Standardization
matI      <- mxMatrix( type="Iden", nrow=nv, ncol=nv, name="I")
invSD     <- mxAlgebra( expression=solve(sqrt(I*V)), name="iSD")
# Calculate genetic and environmental correlations
corA      <- mxAlgebra( expression=solve(sqrt(I*A))%&%A, name ="rA" ) #cov2cor()
corC      <- mxAlgebra( expression=solve(sqrt(I*C))%&%C, name ="rC" )
corD      <- mxAlgebra( expression=solve(sqrt(I*D))%&%D, name ="rD" )
corE      <- mxAlgebra( expression=solve(sqrt(I*E))%&%E, name ="rE" )
# 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, matI, invSD,
                  pathA, pathC,pathD, pathE, covA, covC,covD, covE, covP, corA, corC,corD, corE)
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','D','E','SA','SC','SD','SE'),each=nv)
estVC     <- mxAlgebra( expression=cbind(A,C,D,E,A/V,C/V,D/V,E/V), name="VC", dimnames=list(rowVC,colVC))
# Create Confidence Interval Objects
ciADCE <- mxCI(c( "MZ.rA", "MZ.rC", "MZ.rE","MZ.A","MZ.C","MZ.E","VC"))
# Build Model with Confidence Intervals
modelADCE  <- mxModel( "twoACDEca", pars, modelMZ, modelDZ, multi, estVC, ciADCE )
# ------------------------------------------------------------------------------
# Run ACE Model
fitADCE    <- mxTryHard( modelADCE, intervals=F )
sumADCE    <- summary( fitADCE )
# Compare with Saturated Model
mxCompare( fit, fitADCE )
# Print Goodness-of-fit Statistics & Parameter Estimates
# ------------------------------------------------------------------------------
modelACE   <- mxModel( fitADCE, name="twoACEmodca" )
modelACE <- omxSetParameters(modelACE, labels=c("d11","d22","d33"),free=FALSE, values = 0)
fitACE     <- mxTryHard( modelACE, intervals=F )
mxCompare( fitADCE, fitACE )
# ------------------------------------------------------------------------------
modelADE   <- mxModel( fitADCE, name="twoADEmodca" )
modelADE <- omxSetParameters(modelADE, labels=c("c11","c22"),free=FALSE, values = 0)
fitADE     <- mxTryHard( modelADE, intervals=F )
mxCompare( fitADCE, fitADE )
# Run AE model
modelAE   <- mxModel( fitADCE, name="twoAEca" )
modelAE <- omxSetParameters(modelAE, labels=c("d11","d22","d33","c11","c22"),free=FALSE, values = 0)
fitAE     <- mxRun( modelAE, intervals=F )
mxCompare( fitADCE, fitAE )
mhunter's picture
Joined: 07/31/2009 - 15:26
Select using the multivariate model

Hi Juan,

As I understand the question, it seems like you'd like advice about selecting ACE vs ADE vs AE models when you have 5 phenotypes. My recommendation (and others are welcome to join in with theirs) is to basically ignore the single-phenotype results. Rather, run the model selection based on all five phenotypes. For the 5-phenotype model to run, I'd start with the least theoretical BG model: the Cholesky. Run Cholesky models with ACE, ADE, and AE components. See which seems to be the best description of the data.

You might consider using the umx package for much of this. It's quite easy to specify these models with far less error-prone code, and you still get OpenMx running it underneath.


twolf's picture
Joined: 04/24/2020 - 10:51
Can you actually run an ACE-ADE-model?

Hi! I stumbled by chance over this post and I am curious about the approach of Juan as I could not find any reference to it in the literature though the underlying problem ought to happen from time to time: What do you do in a multivariate model if one of your variables has a strong C-component while another one exhibits no C but significant non-additivity? Can you theoretically fit a multivariate model with a C-component for the former and a D-component for the latter variable as Juan tried? And either way - what would you make of the fact that parameters in the multivariate model change drastically compared to the univariate models? Does this indicate an issue with either the specification of the multivariate or the univariate model(s) or can such a shift be interpreted in a theoretically sound way?

Thanks for your help!

AdminRobK's picture
Joined: 01/24/2014 - 12:15
Can you theoretically fit a multivariate model with a C-component for the former and a D-component for the latter variable as Juan tried?

Sure. You just have to be careful that the appropriate parameters are fixed to zero, for model identification.

And either way - what would you make of the fact that parameters in the multivariate model change drastically compared to the univariate models? Does this indicate an issue with either the specification of the multivariate or the univariate model(s) or can such a shift be interpreted in a theoretically sound way?

Maybe in some cases it would. But look at it this way. If you go from fitting five monophenotype models to fitting one pentaphenotype model as Juan did, you suddenly go from decomposing the variance of one trait at a time to decomposing both the the five traits' variances and their covariances. That adds a lot of new information! Besides, you're also now estimating more free parameters from the same-size sample, so your parameter estimates will be subject to more sampling error.

twolf's picture
Joined: 04/24/2020 - 10:51

Fascinating. I'm looking forward to experiment a little bit with this approach. Thanks!