Model-averaged point estimates

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Joined: 04/17/2019 - 08:58
Model-averaged point estimates

Hi,

I am trying to calculate the heritability for some fat-related traits. I have fitted the ACE model and some submodels (CE and AE) and then learned that it was recommended to use  mxModelAverage() to gain the model-averaged point estimates.

Here is part of the script I am using to fit ACE model:

modelbase <- mxModel("base",
mxMatrix(type="Full",nrow=1,ncol=ncv,free=TRUE, values=0,labels=c('Bage','BSUBTOT_MASS'), name="B" ),
mxMatrix( type="Full", nrow=1, ncol=ntv, free=TRUE, labels="mean", name="meanG" ),
# Matrices declared to store a, c, and e Path Coefficients
mxMatrix( type="Lower", nrow=nv, ncol=nv, free=T, values=sqrt(svace), label="a11",lbound=0.0001, name="a" ),
mxMatrix( type="Lower", nrow=nv, ncol=nv, free=T, values=sqrt(svace), label="c11",lbound=0.0001, name="c" ),
mxMatrix( type="Lower", nrow=nv, ncol=nv, free=T, values=sqrt(svace), label="e11",lbound=0.0001, name="e" ),
# Matrices generated to hold A, C, and E components and total Variance
mxAlgebra( expression=a %*% t(a), name="A" ),
mxAlgebra( expression=c %*% t(c), name="C" ),
mxAlgebra( expression=e %*% t(e), name="E" ),
mxAlgebra( expression=A+C+E, name="V" ),
mxAlgebra( expression=A/V, name="h2" ),
mxAlgebra( expression=C/V, name="c2" ),
mxAlgebra( expression=E/V, name="e2" ))

And the code I'm using to calculate the model-averaged point estimates is as follows:

mxModelAverage(reference=c("base.h2[1,1]","base.c2[1,1]","base.e2[1,1]"), include="onlyFree",
type="AICc", SE=T, models=list(AceFit,AEfit, CEfit))

I learned that, for the purpose of statistical inferences, it's recommended to set include="onlyFree". However, in this way, the sum of model-averaged point estimates of h2, c2 and e2 is not equal to 1. The result is showed as follows:

$Model-Average Estimates Estimate SE base.h2[1,1] 0.6400199 0.14768808 base.c2[1,1] 0.2225559 0.11887596 base.e2[1,1] 0.2259699 0.02830278$Model-wise Estimates
ACE        AE        CE
base.h2[1,1] 0.5502440 0.7759045        NA
base.c2[1,1] 0.2225497        NA 0.6412221
base.e2[1,1] 0.2272063 0.2240955 0.3587779

$Model-wise Sampling Variances ACE AE CE base.h2[1,1] 0.0154727014 0.000742769 NA base.c2[1,1] 0.0141290903 NA 0.001150016 base.e2[1,1] 0.0008354342 0.000742769 0.001150016$Akaike-Weights Table
model      AICc      delta AkaikeWeight inConfidenceSet
1   ACE  995.5385  0.0000000 6.021586e-01               *
2    AE  996.3675  0.8289793 3.978325e-01               *
3    CE 1017.7799 22.2413237 8.913921e-06

Thus, what do you think can be done to fix it? Using include="all" at the cost of violating normal sampling distribution?

Additionally, according to the code of the ACE model, it seems also feasible to calculate model-averaged point estimates of path coefficients a, c, e and variance of A, C, E. However, this will also result in different estimates of heritability. In this case, what parameters do you recommend to be calculated model-averaged point estimates?

Many thanks in advance!

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Joined: 01/24/2014 - 12:15
raw variance components
In this case, what parameters do you recommend to be calculated model-averaged point estimates?

I think it makes the most sense to report model-averaged estimates for the raw variance components--that is, the unstandardized variances of A, C, and E.

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Joined: 04/17/2019 - 08:58
The CI of heritability

Many thanks for your suggestion!
Just to check, if I calculate the model-averaged point estimates of A, C, and E, then I can only get the point estimate of heritability, rather than the CI of it. Is it right? Thank you.

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Joined: 01/24/2014 - 12:15
heritability
Just to check, if I calculate the model-averaged point estimates of A, C, and E, then I can only get the point estimate of heritability, rather than the CI of it. Is it right?

Yes, that's true, if you use include="onlyFree" and refAsBlock=FALSE. If you instead use include="all" and refAsBlock=TRUE, you'll get the joint sampling covariance matrix of the model-averaged A, C, and E variance components. You can then use that joint covariance matrix to calculate the standard error of the heritability coefficient, using the delta method.

Per Chebyshev's Inequality, ±5SEs will give you a confidence interval with coverage probability of at least 96%.