[R-sig-ME] interpretation of an individual-level random effect

[Ben Bolker]

Dominique CARVAL <dominique.carval at ...> writes:

> This is my first post to r-sig-mixed-models project and I hope I am
> sending my message to the appropriate place.
> 
> I have used a binomial GLMM with a logit link function to assess possible
> significant effect of variables (fixed effects: patch density, sex ratio,
> ) on the probability for a weevil to move from its local patch to a
> neighboring patch.
> 
> I have repeated measures (of the same individuals) of the binary response
> of the weevils (to move or not to move) to variations in the local
> conditions of patches.
> 
> To take into account the individual variation (the propensity of a
> particular individuals to respond 1 or 0), I added an individual-level
> random term (the Id of the individuals) to my model. If I have weel
> understood, it is also a way to deal with overdispersion in the data.
> 
> In the summary of GLMM (I used the glmer function of the lme4 package), I
> found the estimate of the variance of the individual-level random term.
> 
> My questions are : Can I interpret this variance as an (real) estimation
> of the variability between individuals in the response (the dispersal
> decision) ?  Can I use this value to simulate individual variability in an
> Individual-Based Model ?

  This all seems quite reasonable.

  You are of course making the assumption that the among-individual
variability is normally distributed on the logit scale.

  If you're going to build an individual-based model anyway you could
use it to test your assumption: specify a particular logit-Normal
distribution of among-individual variation in propensity to disperse,
run the model, simulate an observation process, and see whether running
the statistical model gives you a decent estimate.  (You might want
to do this many times to get a sense of the bias and variance.)

  You could also run the IBM with non-logit-Normal variation
(e.g. several discrete classes of individuals) and see how well
or poorly the glmer fit performs -- does it get the fixed effect
right?  What does it say about the variability?  etc.