I am fitting a glmm for count data as follow:

glmmTMB(counts ~ treatmens + vegetation + days + (1 + treatments|sites), data = data, family = nbinom1, ziformula = ~1))

As far as I understand the glmmTMB manual this means that I think that the effect of treatments varies across sites, and that the zero-inflation is assumed to be constant across data. However, I would like to model it in a way that the zero-inflation will vary by sites. Now I am a bit confused on how to specify this in the model, something like:

ziformula = ~sites or ziformula = ~(1|sites).

It is a bit hard for me to grasp the differences


I think the answer here is not different from any other "should it be fixed or random" decision: are you explicitly interested in which sites have a significantly higher probability of absence, or do you simply want to account for the fact that the probability of absence may vary among them?

See also:

What is the difference between fixed effect, random effect and mixed effect models?


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