Computing pair-wise associations of fixed effects in gLMM

I'm a bit confused by your question -- you "suddenly" introduce multiple
response variables but don't describe what they represent. This is just
as important as describing your predictors! Otherwise we have no way of
knowing where e.g. the Poisson distribution is a reasonable assumption.

Also, note that really shouldn't test normality of your response
variable for two reasons. First, as the size of your data increases, it
becomes easier and easier to reject the null hypothesis of normality for
trivial reasons. No real data is perfectly normally distributed, even
data generated from a normal distribution and so the test rejects more
and more data that really would be fine. Second, it's not the "absolute"
(or more precisely, marginal) distribution of your data that matters,
but rather the distribution of the residuals (or equivalently, the
conditional distribution).

I'm also not clear what you mean with pairwise correlation of
categorical predictors -- do you mean the correlation of fixed-effects
estimates? lme4 will give you that information, but I don't know if
that's what you're looking for. Are you looking for how much the effects
of the different (levels of the different) factors correlate with each
other?

That doesn't yet help you that much, but if you clarify a bit, maybe we
can help you more! :)

Best,
Phillip

Computing pair-wise associations of fixed effects in gLMM

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