[R-sig-eco] Unbalanced data and random effects

[Krzysztof Sakrejda]

On Wed, Oct 16, 2013 at 6:41 AM,  <v_coudrain at voila.fr> wrote:
> Dear all,
>
> I performed a census of insects at different sites and measured there size. I would like to know if size is related to an environmental factor. I modelled the size as a
> fonction of the factor with site as a random variable to account for within-site variability. However I have strong unbalanced data with some sites having only two
> individuals and others up to 100. Is having site as a random factor sufficient to deal with this strong data unbalance?

I'm not sure what you mean by "deal with", but reading about shrinkage
in random effects models in any decent source would probably be a fine
start for you, either here:

http://www.amazon.com/Effects-Extensions-Ecology-Statistics-Biology/dp/0387874577/ref=la_B001JRWU88_1_2/192-3027843-3405263?s=books&ie=UTF8&qid=1381929893&sr=1-2

or here:

http://www.amazon.com/Analysis-Regression-Multilevel-Hierarchical-Models/dp/052168689X/ref=sr_1_3?s=books&ie=UTF8&qid=1381929942&sr=1-3&keywords=gelman+bayesian

The short answer is that the site effect will shrink toward the
average site effect for sites with few individuals.

Krzysztof

> The residual fit of the data is quite bad,
> certainly because of the strong difference in variance among sites.

> Would anybody have some advice? Thank you!
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-- 

Krzysztof Sakrejda

Organismic and Evolutionary Biology
University of Massachusetts, Amherst
319 Morrill Science Center South
611 N. Pleasant Street
Amherst, MA 01003

work #: 413-325-6555
email: sakrejda at cns.umass.edu