covariances between non normal traits

Dear Celine, dear list,

That kind of multivariable modeling is (relatively) easy to do in 
(Win)BUGS/JAGS, by programming a logistic model for each trait, whose 
linear predictor could be modeled as (say) a multivariate normal. This 
could provide some kind of comparison standard to which you could compare 
other results obtained by (say) maximum likelihood (see for example the 
dclone package for a possible approach).

I'd recommend you take a look at Gelman's & Hill's (2007) book on 
multilevel regression, whose part 2 discusses that kind of Bayesian 
modeling. Using "weakly informative" priors (e. g. inverse-Wishart priors 
for variances) should give you estimations (point estimates and 
credibility intervals) close to those of a frequentist analysis (but no p-
values : for that, you'll have to do that yourself (not easily : ask 
Douglas Bates...) or resort to Bayes factors). 

HTH,

					Emmanuel Charpentier

On Fri, 23 Mar 2012 12:22:57 +0100, Celine Teplitsky wrote?:

Dear all,

I have seen this post by Arthur Gilmour in an ASReml related forum:

GLMM models have only been developed for the case of a single GLMM
trait. It is difficult to conceive what is the appropriate error
structure for bivariate GLMM traits when the variances are defined as
functions of the mean.

I would like to know what people on this list think about these issues
e.g. if we want to estimate correlations between 2 traits with a poisson
distribution, are there some special issues to take into account?

Thanks a lot in advance for your help,

All the best

Celine