[R-sig-ME] assessing GLMM fixed- and random-effects for their relative importances (dominance analysis, variation partitioning etc.)

[Thomas Mang]

Dear newsgroups,

I have fitted a Poisson-GLMM (species counts) using lme4. The model's 
fixed-effect predictors (about a dozen in total, possibly with selected 
interactions) can be logically split into 4 major measurement categories 
(e.g. biogeographic variables, climatic variables, etc.). The model has 
three "regular" random factors (spatial/measurement clustering groups), 
plus an additional observation-level random factor due to otherwise 
heavily pronounced Poisson overdispersion; sample size is fairly large 
(several hundreds).

What I would like to do now is, quite untechnically speaking (please 
also apologize if some points may appear a bit naive):
1) contrast the overall "role" of the fixed-effects vs. the 
random-effects on the outcome
2) for the fixed-effects, assess the"importance" of each group of predictors
3) for the random-effects, assess how each random factor shapes outcome 
variation
Note: none of the questions aims at significance testing; given the 
fitted model it's about quantifying (e.g. proportional values) in how 
far each major model component (i.e., each major measurement category of 
fixed-effects and the random factors) influences/explains outcomes. With 
respect to the observation-level random-effect, I am much inclined to 
treat it in the same manner as the three "regular" random factors, 
thereby representing the individual-level variation (as opposed to 
considering it a mere technical means for overdispersion handling and to 
be skipped from above assessments).

Now I am a bit stuck as to which methods are most suited for each 
assessment kind, and the availability of pre-built functions / libraries 
for calculations. What I have roughly come up with so far:
With respect to bullet 2), I suppose dominance analysis for GLMMs would 
be right thing to do. However, I haven't found an R package which could 
perform that for lme4 models. Alternatively, I could calculate AIC 
importance weights for models including/omitting each fixed-effects 
category, but this may be less direct.
With respect to bullet 3), I suppose variation partitioning is the right 
way, but again I haven't found a package for GLMMs. Maybe the easiest 
approach is simply relating the magnitudes of the fitted random-effect 
variances against each other and their sum, thus splitting the total 
random-effects variation (at the link scale) into the individual 
contributions.
With respect to bullet 1), great question. I could fit a model with and 
without fixed-effects, but I fail to see how I would subsequently have 
to relate these models to yield the desired statements. I could 
calculate an R2-measure (e.g. Nakagawa & Schielzeth 2013, A general and 
simple method for obtaining R2 from generalized linear mixed-effects 
models, Methods in Ecolocy and Evolution) and relate the marginal and 
conditional R2 (or, generally speaking, contrasting different sums of 
model terms for "explaining" variance), but this also appears fairly 
indirect, approximative at best.

Any pointers are much appreciated to make it "smell least hacked 
together", both with respect to the general statistical options on the 
market as well as specific packages/implementations for calculations. If 
results can be graphically presented (e.g. Venn's diagrams) that would 
also be great!
If required, I could also fit models using MCMCglmm or glmmADMB if that 
would resolve technical handicaps which could not be overcome by lme4 fits.

best regards and many thanks,
Thomas