Dear Jose,
yes, I would run a single model for all three. If you like, then you can still keep the parameters for all 3 taxon groups completely separated. In that case, you will get identical estimates as if you would get when you fitted 3 separate models, one for each
group. However, fitting a single model greatly simplifies computation of derived quantities, such as sums of the z matrices (a.k.a., species richness). In addition, perhaps it makes sense to have some shared parameters across these groups, notably perhaps
in the detection model, if some factors (weather ? camera malfunction, .... ?) may affect all of them in a similar way.
Best regards --- Marc
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