clusters in zero-inflated negative binomial models
Lies Durnez <ldurnez <at> itg.be> writes:
I want to build a model in R based on animal collection data, that look like
the following
Nr Village District Site Survey Species Count 1 AX A F Dry B 0 2 AY A V Wet A 5 3 BX B F Wet B 1 4 BY B V Dry B 0
Each data point shows one collection unit in a certain Village, District, Site, and Survey for a certain Species. 'Count' is the number of animals collected in that collection unit. It is possible that zero animals are collected in that unit because of very low densities, but also because of climatic conditions (wind, rain, etc), so we would expect an excess in zeroes. I have tested that the data are overdispersed (variance much bigger than mean), so a zero-inflated negative binomial model seems the most suitable model in this case.
[snip snip snip]
However, the animal collections were only done in 4 districts, and in each district 3 villages were chosen (a total of 12 villages). This should be included in the design. The package survey allows this for the standard negative binomial model, but it seems to me that it is not possible for the zero-inflated NB. So, my question is two-fold: 1. Is a zero-inflated NB possible in the survey package. If yes, how? 2. If no, how can I build a zero-inflated NB model that takes into account the clustering of the observations (animal counts) in villages and the clustering of the villages in districts.
Treating villages and districts as random effects (clusters) basically puts you in the domain of generalized linear mixed models. You can use the glmmADMB package to fit zero-inflated, mixed negative binomial models. You can also use the MCMCglmm package to fit lognormal-Poisson models, which are another form of overdispersed count data (it depends how strongly you require that the actual model be NB as opposed to just a reasonable model for overdispersed count data). 4 districts is not very many for estimating an among-district variance (which is basically what you are doing when you fit a clustered/ mixed model), so I might suggest using district as a fixed effect, but then using district:village (i.e. the interaction between district and village, or village alone if they are uniquely labeled). http://glmm.wikidot.com/faq may be useful. I would suggest that you send follow-ups to the r-sig-mixed-models <at> r-project.org mailing list.