[R-sig-ME] Bayesian counterpart to NPMLREG

[Jarrod Hadfield]

Dear Shige,

I am not sure what is meant by "mass points for the random component"  
so can't really say whether it is better or worse than assuming a  
Gaussian distribution for the random effects. With regard to your  
second question - MCMCglmm assumes the random effects follow a  
Gaussian distribution on the link scale, and does not allow an other  
option. The hglm package would allow different distributions though.

Note that unless you have rescaled your terms by your choice of  
residual  variance (the response is binary, right?) then you should  
not expect MCMCglmm to give you the same answer as lme4 (and NPMLREG  
probably).

Cheers,

Jarrod


On 9 Apr 2010, at 14:28, Shige Song wrote:

> 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
>
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