[R-sig-ME] MCMCglmm poisson / not poisson

[Jarrod Hadfield]

Hi,

The residuals (pre observation random effects) are assumed to be  
conditionaly normal. However, I think that even if this is satisfied  
then this does not imply that the posterior means/modes of the random  
effects will be normal. In fact when the expected number of counts is  
small I could imagine that the posterior means/modes could be strongly  
non-normal, perhaps even multimodal. Are the "latents" the posterior  
mean/mode of the residuals?  If you plot the distribution of  
per-observation  random-effects on an iteration by iteration basis, do  
you still see non-normality?

Cheers,

Jarrod


Quoting Mikhail Matz <matz at utexas.edu> on Tue, 28 Aug 2012 22:06:45 -0500:

>
> Hello -
>
> I am playing with ways to justify that the MCMCglmm model fits my  
> data well, which is quite important for me since I am hoping to be  
> able to suggest MCMCglmm-based modeling as a general solution for a  
> particular type of analysis.
>
> I am running "poisson" family on counts data, with two random  
> effects. Following Elston, D. A., R. Moss, et al. (2001).  
> Parasitology 122: 563-569., I am checking whether my lognormal  
> residuals (latent variable minus predicted value) are normally  
> distributed (check), if my random effects (saved with pr=T) are  
> normally distributed (more or less check), and then I try to see if  
> the observed counts really look like Poisson samples based on the  
> latent variables. Again, following Elston et al, I am making a p-p  
> plot using this script (expert coders, please don't judge):
>
> pp.poisson=function(counts,latents) {
> 	sim=c()
> 	for(i in 1:length(counts)){
> 		if (is.na(counts[i])) next
> 		data=counts[i]
> 		low=ppois(data,exp(latents[i]))-dpois(data,exp(latents[i]))
> 		up=ppois(data,exp(latents[i]))
> 		ss=seq(low,up,(up-low)/100)
> 		sim=append(sim,sample(ss,1))
> 	}
> 	sims=sort(sim)
> 	xx=(rank(sims)-0.5)/length(sims)
> 	plot(sims~xx)
> 	abline(0,1)
> }
>
> … and unfortunately it looks really ugly, like a very strongly bent   
> ' ~ ' rather than a line.
> The little script above seems to work; here is a sanity check:
>
> psim=c()
> nnn=rnorm(500,10,10)
> for (i in 1:length(nnn)){
> 	psim=append(psim,rpois(1,exp(nnn[i])))
> }
> pp.poisson(psim,nnn)
>
> I will be extremely grateful for any comments on this.
>
> cheers
>
> Misha
> UT Austin
>
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>
>



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