Model-averaged point estimates

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

$`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!