[R-sig-ME] Non normal random effects

Douglas Bates bates at stat.wisc.edu
Mon Nov 29 20:12:31 CET 2010

On Mon, Nov 29, 2010 at 9:02 AM, Gustavo Betini <betinig at uoguelph.ca> wrote:
> Lets say that I want to look at the interaction between Species and some other variable...Temperature. The right specification would be
> (Temperature|Species) + (Temperature|Station:Species)
> or simply
> (1|Species) + (Temperature|Station:Species)

That depends on whether you feel that the changes in temperature
coefficient would be associated with the Species or with the
Station:Species combination or both.  I would try to start simply,
perhaps with

(1 + Temperature|Species) + (1|Station:Species)

It is difficult to estimate a large number of variance components
without a lot of data.  Starting with the "sumo" model that has every
possible term and interaction then seeing if you can pare it back
makes more sense in fixed-effects models than in mixed-effects models.
 Deletion strategies are easier to describe and evaluate when working
with fixed-effects only.  Also, in the fixed-effects case having a
model with too many terms in it doesn't usually prevent estimation of
coefficients, it just make the estimators less precise.

In a mixed-effects model, adding interaction terms increases the
number of variance-component parameters quadratically, not linearly.
And it is a lot more difficult to determine that the
variance-covariance matrix of the random effects is singular than to
detect that a model matrix is rank deficient.

So I would recommend building mixed-effects models using forward
selection, not backward selection, and proceeding cautiously.

> Thanks,
> Gustavo S. Betini
> Dept. of Integrative Biology
> University of Guelph, Canada
> On 10-11-27 12:04 PM, Douglas Bates wrote:
> Just in terms of the model specification, do you really mean
> (1|Species/Station)?  That expands to
>  (1|Species) + (1|Species:Station)
> and wouldn't reduce to (1|Station) in a model specification.  I think
> you meant "species within station", which would be written as
> (1|Station/Species) although I prefer the more explicit form
> (1|Station) + (1|Station:Species)
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