Selecting a subset of data for binary mixed model

Dear List,

I'm using MCMglmm to estimate heritability for binary traits with the model
below. Currently, it is not computationally feasible to use all data in the
model. I'm wondering what would be a good strategy to sample a subset of
data?

I'm currently selecting a subset of individuals with longer observation
periods (i.e. increased chance to observe traits). Would this strategy
introduce bias in the estimates? Should I just randomly sample a subset?

priorA <- list(R = list(V = 1, fix = 1), G = list(G1 =list(V = 1, nu =
1000, alpha.mu = 0, alpha.V = 1), G2 =list(V = 1, nu = 1000, alpha.mu = 0,
alpha.V = 1)))

modelbin <- MCMCglmm(pheno ~ sex + age, random = ~animal +fam , family =
"threshold", pedigree = pedigree, prior = priorA, data = databin, nitt =
nitt, burnin = burnin, thin = 500, slice=TRUE, pl=TRUE)

Sex and age are factor variables. The fam variable is for the common
environment effects in the descendants. All parents have their own fam
value.

Any help would be greatly appreciated.

Best,
Kanix Wang