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ADE and submodels

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YiTan's picture
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Joined: 10/08/2014 - 05:28
ADE and submodels

Hi all,

I noticed in the ADE code (http://www.vipbg.vcu.edu/HGEN619_2014/twinAdeCon.R) that the only submodels considered are AE and E models. I would like to ask: why isn't the DE model a possible model to consider?

Thanks and best regards,
Yi Ting

tbates's picture
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Joined: 07/31/2009 - 14:25
No representation without taxation (no D without A)

> I noticed in the ADE code that only AE and E models are considered
> why isn't the DE model a possible model to consider?

It's considered unlikely that all genes for a behavior will be non-additive, with no additive effects.

One can imagine such a trait – simplistically coded eye colour, for instance – which consists of a single Mendelizing dominant allele + unshared noise (DE).

But for polygenic traits, it's hard to generate data from plausible sets of gene alleles where the trait doesn't show an additive signal.

So the reasonable model is ADE, with A droppable only due to lack of power.

Often people will drop D leaving an AE model. This, no doubt also commonly reflects lack of power also, with the null hypothesis of strictly zero D being unlikely also for traits that have seen any selection.

The choice of including D OR C is, of course, invidious.

Recently people (Zuk et al.) have suggested that reduced DZ similarity due to D (perhaps gene-gene interaction) combined with increased DZ similarity due to C might make AE twins reared together models fit better than they should (if, say, we had adoption data in the mix).

Does anyone have the (Purcell? Neale?) ref on where unmodelled variance goes in twin studies - that's worth citing here.

It would be interesting if your DE model fit better than AE. I would mount a statistical argument against that on the principle of marginality: the principle of not including interactions (which D is) in the absence of main effects to ensure that main effect variance is not aliased into the interaction term. i.e., dropping the degree of freedom might work in terms of AIC, but is fraught in causal terms.

Just for completeness, this question typically arises from a researcher who wants to test not a DE model, but a DCE model (i.e., to retain shared environment and drop additive genetic effects).

I think (others might chime in) that the logic arguing against this is that an inability to identify the model we should use (ADCE) is not justification for using a model (by the argument above from additivity) that we think is implausible (DE or DCE).

See also this paper from the always-worth-reading Neil Risch for an explanation of the related expectation that we should not (commonly) expect mechanistic interactions in the absence of main effects (here in the context of a critique of GxE interactions for depression.

http://www.ncbi.nlm.nih.gov/pubmed/19531786

YiTan's picture
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Joined: 10/08/2014 - 05:28
My DE model does appear to fit better than ADE and AE model

Hi Tim,

Thank you very much for the very comprehensive explanation. My DE model does appear to fit better than the ADE and the AE model. Here's the output from my Het5 ADE model (in terms of lowest AIC).

                  base comparison ep minus2LL  df      AIC    diffLL diffdf        p
1    Saturated QualADE       <NA> 25 640.3550 189 262.3550        NA     NA       NA
2    Saturated QualADE    QualADE 10 655.2017 204 247.2017  14.84669     15 0.462516
3    Saturated QualADE    QuanADE  9 655.2017 205 245.2017  14.84669     16 0.5358948
4    Saturated QualADE    HomoAde  6 656.3535 208 240.3535  15.9985     19 0.6573781
 
     base comparison ep minus2LL  df      AIC        diffLL diffdf         p
1 QualADE       <NA> 10 655.2017 204 247.2017            NA     NA        NA
2 QualADE    QuanADE  9 655.2017 205 245.2017 -2.160050e-12      1 1.0000000
3 QualADE    HomoAde  6 656.3535 208 240.3535  1.151812e+00      4 0.8859669
 
     base comparison ep minus2LL  df      AIC        diffLL diffdf            p
1 HomoAde       <NA>  6 656.3535 208 240.3535            NA     NA           NA
2 HomoAde         AE  5 659.2153 209 241.2153  2.861769e+00      1 9.070767e-02
3 HomoAde         DE  5 656.3535 209 238.3535 -9.129053e-11      1 1.000000e+00
4 HomoAde          E  4 704.8698 210 284.8698  4.851634e+01      2 2.916162e-11
 
confidence intervals for ADE model:
                  lbound     estimate    ubound note
HomoAde.SAf          NA 1.799437e-12 0.7380858  !!!
HomoAde.SDf 1.810121e-43 6.916090e-01 0.7860932     
HomoAde.SEf 2.139068e-01 3.083910e-01 0.4427758     
HomoAde.SAm          NA 1.799437e-12 0.7380858  !!!
HomoAde.SDm 1.810121e-43 6.916090e-01 0.7860932     
HomoAde.SEm 2.139068e-01 3.083910e-01 0.4427758     

As can be seen from above, the A estimate is negligible whereas the D estimate is really high. If I understand your advice correctly, it's best if I choose the AE model over the DE or ADE model, because main effect variances are more important?

I've attached my entire R code and in particular, I would like to confirm whether this part of my code is correct?

meanGf  <- mxAlgebra( Mean + AgeR + SexR , name="expMeanGf")
meanGm  <- mxAlgebra( Mean + AgeR + SexR , name="expMeanGm")
meanGfm <- mxAlgebra(expression= cbind(expMeanGf[,1], expMeanGm[,1]), name="expMeanGfm")
 
 
defs      <- list( intercept, defSex, B_Sex, meanSex, defAge, B_Age, meanAge)
 
covMZf    <- mxAlgebra( expression= rbind( cbind(Vf, Af+Df), cbind(Af+Df, Vf)), name="expCovMZf" )
covDZf    <- mxAlgebra( expression= rbind( cbind(Vf, 0.5%x%Af+0.25%x%Df), cbind(0.5%x%Af+0.25%x%Df, Vf)), name="expCovDZf" )
covMZm    <- mxAlgebra( expression= rbind( cbind(Vm, Am+Dm), cbind(Am+Dm, Vm)), name="expCovMZm" )
covDZm    <- mxAlgebra( expression= rbind( cbind(Vm, 0.5%x%Am+0.25%x%Dm), cbind(0.5%x%Am+0.25%x%Dm, Vm)), name="expCovDZm" )
 
 
CVfm      <- mxAlgebra( expression= 0.5%*%rg%x%(af%*%t(am))+0.25%*%df%*%t(dm), name="CVfm" )
CVmf      <- mxAlgebra( expression= 0.5%*%rg%x%(am%*%t(af))+0.25%*%dm%*%t(df), name="CVmf" )

Thanks and best regards,
Yi Ting