[R-sig-ME] assessing GLMM fixed- and random-effects for their relative importances (dominance analysis, variation partitioning etc.)
Thomas Mang
firespot71 at gmail.com
Thu Apr 21 21:46:09 CEST 2016
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
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