[R-sig-ME] Poisson or Gaussian when modelling count data + heteroscedasticity in predictor variables

[Luciana Motta]

Hello,

my name is Lucy, and I'm studying richness of aquatic insect in lakes. I
took samples from different habitats in each lake, for which I though of a
mixed model with my predictors as fixed effects, and lake/habitat as random
effects. I did a model using "glmer", to be able to use Poisson
distribution for residuals, due to my type of response variable (count data
-richness).

But studying the data graphically, I suspected variance heterogeneity in 2
predictors.

I continued doing model selection with glmer with Poisson distribution, but
also made a model using "lmer" (therefore, Gaussian distribution of
residuals), to be able to model variance heterogeneity of those predictors
and see if models fit better with it.

Finally, yes..."lmer" model, with Gaussian distribution and varExp
modelling for the variance of those predictors seem much more adequate than
the "glmer" with Poisson (conclusion I arrived to by studying residuals,
fitted values, qqplot and normality tests).

Can heteroscedasticity be a larger problem to be accounted for, than the
distribution of the errors for count data? I read that sometimes
heteroscedasticity
can be masking what we think is a normality problem. Also that Poisson
distribution accounts for heteroscedasticity....but in my case, model seems
much worse. Is just that since Poisson, Neg.Binom. etc., is so recommended
for count data, that I don't really know if I'm plain wrong in even
considering staying with Gaussian. Any suggestions/further readings about
this?

Thank you very much,

-- 
Luciana M. Motta
Licenciada en Cs. Biológicas FCEyN, U.B.A.

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