Hi,

First I'd like to apologize for probably very novice questions: I am new to
this list as well as rather new in the field of mixed model. Jobwise, I am
aquatic/river ecologist (actually PhD student) and not a
statistician/mathematician and so most of my questions are probably related
to the topic of rivers/fish.

I want use a GLMM with presence/absence data (logit-model) as response. The
model contains the binary response (presence/absence of a species at a
site) and 3 continuous predictors (fixed effects: habitat quality,
dispersal metric, metric of influence of barriers) as well as two random
effects (in my case species and sites).  For that purpose I am using the
R-function (g)lme from the package lme4.

Now several questions appeared:

1) My predictors are partly highly skewed:
> summary(Pred1)
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max.
  0.0000   0.0000   0.1143   9.0720   3.8400 616.4000
> summary(Pred2)
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max.
 -7.44400  -0.00031   0.00000   0.41560   0.00019 255.70000
> summary(Pred3)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
 0.0000  0.1221  0.3716  0.3734  0.5914  0.9626

In a standard regression model they would definitely need transformation
(e.g. log).
Is that the first step in a logistic mixed model too?

2) As I am interested in a way to compare the relative size effects of the
three predictors I had been referred to the simple approach of Schielzeth
2010 (thank you for that tip Mr. Bolker!). In this article it is
recommended to scale the predictors for comparison of their importance
and/or to scale and center in case one also wants to model interactions
between continuous predictor variables.
So my question how would that interfere with any transformation of the
variables as described in my first question? And what is the correct order:
first transformation than scaling?

3) After reading some list posts like this here:
https://stat.ethz.ch/pipermail/r-sig-mixed-models/2011q1/015591.html I
learnt that comparing two lmer-models (likelihood ratio test with anova())
is the way to find out if a predictor or interaction is significant in a
model. Thus this method (comparing complex with less complex) models can
lead to the most parsimonious model comprising only of the most important
predictors and interactions. After reading Schielzeth 2010, I think this
comparison test should be made with centered and scaled variables (and if
needed transformed before)?

4) This brings me than to my final interpretation of the results. In
relation to that I came across the post as mentioned before and a tutorial:
http://www.ats.ucla.edu/stat/mult_pkg/faq/general/odds_ratio.htm  I think
that tutorial really helped me to understand the meaning of odds etc. But
how can odds be interpreted if the predictors were transformed before?

First I'd calculate the final parsimonious model once with transformed and
scaled predictors to get an idea about the relative impact of each
independent predictor. Second, the same model with transformed but with
unscaled predictors can provide absolute parameter estimates for the odds.

Maybe someone of you can enlighten me so that also an ecologist uses glmms
in a correct way and I can use it to interpret my data.

Thank you so much!

Best regards,
Johannes

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