Fitting beta-binomial overdispersed model with random effects (repeated measures)

[blf]

Hello -

I have been looking and can't find out how to fit a beta-binomial model with random effects (subject).

In FFM there is a beta-binomial model but looks like no random effects.

In glimmix there is binomial with random effects but no over-dispersed binomial (beta-binomial). 

Anyone had experience fitting this model in SAS?

[SteveDenham]

If you know the formulas for the log-likelihood, you can, with no small amount of effort, write the supporting code to fit a beta-binomial in NLMIXED or in MCMC, where you make the binomial parameter a function of the beta distribution. Mr. Google might be of some assistance here. I suppose I am saying I know what might work, but I sure don't know how to do it.

SteveDenham

[StatDave]

The log likelihood for the beta-binomial is shown in "Log-Likelihood Functions for Response Distributions" in the Details section of the FMM documentation. As suggested, you can use PROC NLMIXED to fit a model specifying this log likelihood and adding a RANDOM statement if desired. You can see examples of fitting a model with specified log likelihood function in this note showing this using the log likelihood for the truncated Poisson and negative binomial distributions and in this note where the zero-inflated Poisson and negative binomial are specified.

[blf]

Hello - 

Thank you for this suggestion. I have the NLMIXED model working for a beta-binomial  with random effects (intercept) but for some datasets where the N is large (>150) it is failing to compute I think due to the factorial and beta functions in the beta-binomial distribution. 

The non-random effects Beta-binomial models works in PROC FMM but not in PROC NLMIXED (no random effects) when counts (N) are large. I have tried different optimization methods and nothing works. 

Any suggestions ?

[StatDave]

When you coded the log likelihood, this might result if you used LOG(GAMMA(...)) instead of the LGAMMA function as shown in the examples I referred to earlier.

[Season]

I have no idea on the solution to this specific question, but would like to recommend the only monograph I have found on building overdispersion models with SAS: Amazon.com: Overdispersion Models in SAS: 9781607648819: Morel PhD, Jorge G., Neerchal PhD, Nagaraj:.... I have read part of it and am not sure whether it contains the answer to your specific question. But I am sure it is a good monograph for those who wish to have a systematic understanding on this field.