[R-sig-ME] Bayesian counterpart to NPMLREG

[Shige Song]

Dear All,

I am comparing two sets of results on involuntary fetal loss from
retrospective pregnancy history. Since each woman may have more than
one pregnancy, it makes sense to analyse it as a two-level logistic
regression with random intercept (at mother-level). One set of results
were obtained from random effect models that assume normal
distribution for the random component (estimated using Lme4 and
NPMLREG with random distribution set to "gh"), the second set of
results were obtained from random effect model that assume a set of
mass points for the random component (estimated using NPMLREG with
random distribution set to "np"). There are some interesting findings.
To be more specific, one interaction term I included (between birth
cohort and place residence) was estimated to be .373 (.202) in random
effect logistic regression assuming normal distribution but .433
(.202) in random effect assuming non-parametric random component. My
reading on this is that, the normal distribution assumption has
downwardly biased the point estimate of this interaction term and the
NPML estimate is more trustworthy.

I also want to do a similar comparison with Bayesian analysis. I have
been playing with MCMCglmm. The mean and the median of the posterior
distribution for that interaction term is .415 and .414, which is in
between of the the parametric and non-parametric ML estimates. Are we
still assuming some parametric distributions for the random component
here? If so, is there a way to further relax such assumption? Any
comments and suggestion are highly appreciated.

Best,
Shige