Parameter contraints across subgroups

Posted on Tue, 09/04/2018 - 16:19

Julia Joined: 03/29/2012

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Hi all,

I am running a simple univariate saturated threshold model to find out the effects of covariates on the variable of interest across three groups - MZ twins, DZ twins and unrelated individuals. The regressions are the following: y ~age + sex + IBS.
As one of the research questions, I would like to specify such a constraint for IBS coefficients: beta_unrel = 2*beta_DZ. This is where I got stuck. I looked at the following thread https://openmx.ssri.psu.edu/thread/446 and wanted to specify an mxAlgebra instead of mxConstraint, but I struggle to modify my original model to test this assumption.

This is the chunk of the code for the regressions from the original model:
meanMZ <- mxMatrix( type="Zero", nrow=1, ncol=ntv, name="expMeanMZ" ) meanDZ <- mxMatrix( type="Zero", nrow=1, ncol=ntv, name="expMeanDZ" ) meanUnrel <- mxMatrix( type="Zero", nrow=1, ncol=ntv, name="expMeanUnrel" )


threMZ 	<- mxMatrix( type="Full", nrow=1, ncol=ntv, free=TRUE, values=.8, labels='threMZ', name="threMZ" )

threDZ 	<- mxMatrix( type="Full", nrow=1, ncol=ntv, free=TRUE, values=.8, labels='threDZ', name="threDZ" )

threUnrel 	<- mxMatrix( type="Full", nrow=1, ncol=ntv, free=TRUE, values=.8, labels='threUnrel', name="threUnrel" )
defAge1    	<- mxMatrix( type="Full", nrow=1, ncol=1, free=FALSE, labels="data.Zage_s_1", name="Age1" )

defAge2    	<- mxMatrix( type="Full", nrow=1, ncol=1, free=FALSE, labels="data.Zage_s_2", name="Age2" )
B_AgeMZ     	<- mxMatrix( type="Full", nrow=1, ncol=nv, free=TRUE, values=.01, label="betaAgeMZ", name="bAgeMZ" )

B_AgeDZ     	<- mxMatrix( type="Full", nrow=1, ncol=nv, free=TRUE, values=.01, label="betaAgeDZ", name="bAgeDZ" )

B_AgeUnrel     	<- mxMatrix( type="Full", nrow=1, ncol=nv, free=TRUE, values=.01, label="betaAgeUnrel", name="bAgeUnrel" )
threAge1MZ   <- mxAlgebra(  Age1%*%bAgeMZ, name="AgeR1MZ")

threAge2MZ   <- mxAlgebra(  Age2%*%bAgeMZ, name="AgeR2MZ")

threAge1DZ   <- mxAlgebra(  Age1%*%bAgeDZ, name="AgeR1DZ")

threAge2DZ   <- mxAlgebra(  Age2%*%bAgeDZ, name="AgeR2DZ")

threAge1Unrel   <- mxAlgebra(  Age1%*%bAgeUnrel, name="AgeR1Unrel")

threAge2Unrel   <- mxAlgebra(  Age2%*%bAgeUnrel, name="AgeR2Unrel")
defSex1    	<- mxMatrix( type="Full", nrow=1, ncol=1, free=FALSE, labels="data.sex_s_1", name="Sex1" )

defSex2    	<- mxMatrix( type="Full", nrow=1, ncol=1, free=FALSE, labels="data.sex_s_2", name="Sex2" )
B_SexMZ     	<- mxMatrix( type="Full", nrow=1, ncol=nv, free=TRUE, values=.01, label="betaSexMZ", name="bSexMZ" )

B_SexDZ     	<- mxMatrix( type="Full", nrow=1, ncol=nv, free=TRUE, values=.01, label="betaSexDZ", name="bSexDZ" )

B_SexUnrel     	<- mxMatrix( type="Full", nrow=1, ncol=nv, free=TRUE, values=.01, label="betaSexUnrel", name="bSexUnrel" )
threSex1MZ   <- mxAlgebra(  Sex1%*%bSexMZ, name="SexR1MZ")

threSex2MZ   <- mxAlgebra(  Sex2%*%bSexMZ, name="SexR2MZ")

threSex1DZ   <- mxAlgebra(  Sex1%*%bSexDZ, name="SexR1DZ")

threSex2DZ   <- mxAlgebra(  Sex2%*%bSexDZ, name="SexR2DZ")

threSex1Unrel   <- mxAlgebra(  Sex1%*%bSexUnrel, name="SexR1Unrel")

threSex2Unrel   <- mxAlgebra(  Sex2%*%bSexUnrel, name="SexR2Unrel")
defIBS1    	<- mxMatrix( type="Full", nrow=1, ncol=1, free=FALSE, labels="data.ibs_gen_s_1", name="IBS1" )

defIBS2    	<- mxMatrix( type="Full", nrow=1, ncol=1, free=FALSE, labels="data.ibs_gen_s_2", name="IBS2" )
B_IBSMZ     	<- mxMatrix( type="Full", nrow=1, ncol=nv, free=TRUE, values=.01, label="betaIBSMZ", name="bIBSMZ" )

B_IBSDZ     	<- mxMatrix( type="Full", nrow=1, ncol=nv, free=TRUE, values=.01, label="betaIBSDZ", name="bIBSDZ" )

B_IBSUnrel     	<- mxMatrix( type="Full", nrow=1, ncol=nv, free=TRUE, values=.01, label="betaIBSUnrel", name="bIBSUnrel" )
threIBS1MZ   <- mxAlgebra(  IBS1%*%bIBSMZ, name="IBSR1MZ")

threIBS2MZ   <- mxAlgebra(  IBS2%*%bIBSMZ, name="IBSR2MZ")

threIBS1DZ   <- mxAlgebra(  IBS1%*%bIBSDZ, name="IBSR1DZ")

threIBS2DZ   <- mxAlgebra(  IBS2%*%bIBSDZ, name="IBSR2DZ")

threIBS1Unrel   <- mxAlgebra(  IBS1%*%bIBSUnrel, name="IBSR1Unrel")

threIBS2Unrel   <- mxAlgebra(  IBS2%*%bIBSUnrel, name="IBSR2Unrel")

expThreMZ <- mxAlgebra( expression= threMZ + cbind(AgeR1MZ,AgeR2MZ) + cbind(SexR1MZ,SexR2MZ) + cbind(IBSR1MZ,IBSR2MZ), name="expThreMZ" ) expThreDZ <- mxAlgebra( expression= threDZ + cbind(AgeR1DZ,AgeR2DZ) + cbind(SexR1DZ,SexR2DZ) + cbind(IBSR1DZ,IBSR2DZ), name="expThreDZ" ) expThreUnrel <- mxAlgebra( expression= threUnrel + cbind(AgeR1Unrel,AgeR2Unrel) + cbind(SexR1Unrel,SexR2Unrel) + cbind(IBSR1Unrel,IBSR2Unrel), name="expThreUnrel" )

All this, together with other entities, go into three subgroups and into the total model:
modelMZ <- mxModel( name="MZ", meanMZ, covMZ, threMZ, defAge1, defAge2, B_AgeMZ, threAge1MZ, threAge2MZ, defSex1, defSex2, B_SexMZ, threSex1MZ, threSex2MZ, defIBS1, defIBS2, B_IBSMZ, threIBS1MZ, threIBS2MZ, expThreMZ, dataMZ, expMZ, funML ) modelDZ <- mxModel( name="DZ", meanDZ, covDZ, threDZ, defAge1, defAge2, B_AgeDZ, threAge1DZ, threAge2DZ, defSex1, defSex2, B_SexDZ, threSex1DZ, threSex2DZ, defIBS1, defIBS2, B_IBSDZ, threIBS1DZ, threIBS2DZ, expThreDZ, dataDZ, expDZ, funML ) modelUnrel <- mxModel( name="Unrel", meanUnrel, covUnrel, threUnrel, defAge1, defAge2, B_AgeUnrel, threAge1Unrel, threAge2Unrel, defSex1, defSex2, B_SexUnrel, threSex1Unrel, threSex2Unrel, defIBS1, defIBS2, B_IBSUnrel, threIBS1Unrel, threIBS2Unrel, expThreUnrel, dataUnrel, expUnrel, funML )


multi     <- mxFitFunctionMultigroup( c("MZ","DZ","Unrel") )

univSatModel <- mxModel("univSat", modelMZ, modelDZ, modelUnrel, multi) univSatFit <- mxRun(univSatModel)

Now I would like to test whether we can impose betaIBSUnrel = 2*betaIBSDZ. I tried the following:
restrModel = mxModel(model1, name='restrM') restrModel = omxSetParameters(restrModel , labels='betaIBSDZ', values=0.01, free=T, newlabels = 'betaIBSDZ') B_IBSDZ_Unrel <- mxMatrix( type="Full", nrow=1, ncol=nv, free=TRUE, values=.01, label="betaIBSDZ", name="bIBSDZ" ) B_IBSUnrel_matrix <- mxMatrix( type="Full", nrow=1, ncol=nv, values=.01, label="bIBSUnrel[1,1]", name="bIBSUnrel_matrix" ) B_IBSUnrel_alg = mxAlgebra(2*betaIBSDZ, name='bIBSUnrel') restrModel = mxModel(GenIBSModel, B_IBSDZ_Unrel, B_IBSUnrel_matrix, B_IBSUnrel_alg) restrFit = mxRun(restrModel)

But this doesn't seem to do the right thing. The new 'bIBSUnrel' from B_IBSUnrel_alg is calculated along the old 'bIBSUnrel' in the Unrel subgroup. This is the summary of the model fit:
> summary(restrFit) Summary of restrM


free parameters:

           name          matrix             row             col    Estimate  Std.Error A

1     betaIBSDZ          bIBSDZ               1               1 -0.13358435 0.13235843

2     covT1T2MZ     MZ.expCovMZ strain_dich_s_1 strain_dich_s_2  0.42856769 0.11593230

3     threshAll       MZ.threMZ               1               1  0.64756220 0.10746847

4     betaAgeMZ       MZ.bAgeMZ               1               1  0.07123071 0.07590719

5     betaSexMZ       MZ.bSexMZ               1               1 -0.14514120 0.14911503

6     covT1T2DZ     DZ.expCovDZ strain_dich_s_1 strain_dich_s_2  0.22069379 0.13846191

7     betaAgeDZ       DZ.bAgeDZ               1               1  0.37860942 0.09224387

8     betaSexDZ       DZ.bSexDZ               1               1  0.07751815 0.14411199

9   threshUnrel Unrel.threUnrel               1               1  0.96161404 0.03937058

10 betaAgeUnrel Unrel.bAgeUnrel               1               1  0.10529660 0.02691893

11 betaSexUnrel Unrel.bSexUnrel               1               1 -0.13111884 0.05280346

12 betaIBSUnrel Unrel.bIBSUnrel               1               1 -0.49658313 0.09702530

> mxEval(c(betaIBSDZ, bIBSUnrel), restrFit) [,1] [1,] -0.1335843 [2,] -0.2671687

You can see that there is still a matrix bIBSUnrel in Unrel group which element was estimated freely (-0.497), whereas the new bIBSUnrel matrix that I created for the submodel is equal to two times betaIBSDZ.

Could you please help me to code this across group constraint and to run a restricted model with it?
Thank you in advance!
Julia

Replied on Tue, 09/04/2018 - 17:07

AdminRobK Joined: 01/24/2014

namespace

Your syntax doesn't work because `B_IBSUnrel_matrix` is going into the container model, not the submodel `modelUnrel`, so the submodel's expectation never "sees" it. Plus, your syntax never fixes the parameter labeled "bIBSUnrel", which is still there in that submodel. I think the easiest thing is probably to just define the regression coefficient for IBS among unrelateds as an algebra,



B_IBSUnrel_alg <- mxAlgebra(2*betaIBSDZ, name='bIBSUnrel')

, or perhaps,



B_IBSUnrel_alg <- mxAlgebra(2*DZ.bIBSDZ, name='bIBSUnrel')

, then redefine `modelUnrel` to use it instead of `B_IBSUnrel`,



modelUnrel   <- mxModel( name="Unrel",

     meanUnrel, covUnrel, threUnrel, defAge1, defAge2, B_AgeUnrel, threAge1Unrel, threAge2Unrel, defSex1, defSex2,

     B_SexUnrel, threSex1Unrel, threSex2Unrel, defIBS1, defIBS2, B_IBSUnrel_alg, threIBS1Unrel, threIBS2Unrel,

     expThreUnrel, dataUnrel, expUnrel, funML )

and then rebuild the multigroup model using the redefined `modelUnrel`.

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Replied on Wed, 09/05/2018 - 16:57

Julia Joined: 03/29/2012

Great!

Hi Rob. Thanks a bunch!!! This does seem to work! Thank you again!

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Replied on Thu, 09/06/2018 - 09:34

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Parameter contraints across subgroups

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Great!

Glad to hear it!

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