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My two separate response (dependent) variables are counts of two mesopredator grouper species on coral reefs. I have tried various models (LM, GLM Poisson and Gaussian and zinf and zinb) both with untransformed response variables and with square root transformed response variables.

The best fit model for one species (due to the distribution of the data) is a Gaussian GLM with square root transformed counts and for the other species is a zero-inflated Poisson model with untransformed counts.

  • Is it appropriate to use different models if I want to compare the effects of the explanatory variables on each of the species?

  • If not, which model can I use to fit both species count data?

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If you want to compare effects then you are going to need your coefficients to be on the same scale. This will require using the same model for both species. I am not particularly familiar with the zero-inflated Poisson model, but I would hazard a guess that it is modeling a similar sort of non-linearity as your sqrt transformed counts in the Gaussian model. One thing you should ask yourself is how much worse is one fit from the other. If the difference between fits is trivial, then I'd say you should go forward using just a single model type. If the difference between fits is huge, then you probably need to think about the issue further. The simple solution would be to model both species using both models. If the comparisons come out the same using either model, then you are probably good to go either way. If the result depends on the comparison you run, then you probably need to think about the generating functions for your data more carefully.

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