[R] clusters in zero-inflated negative binomial models

[Lies Durnez]

Dear all,

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. To be sure, I will compare the zero-inflated model to the standard binomial model using the vuong test. The models will be made for each species separately. For these models I can use the glm.nb(), and the and zeroinfl () in the package pscl, looking something like this (after selection of the subset B<-subset(data, Species=="B")): 
NB=glm.nb(formula = Count ~ District+Site+Survey, data = B)
ZINB=zeroinfl(formula = Count ~ District+Site+Survey, dist="negbin", data = B)
Vuong(NB,ZINB)
I have tried this and it works very elegantly.

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. 

Thank you very much for the help.
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