Possible that "Variation Partitioning" may be an approach that could help in this case. I believe it is capable at least theoretically of dealing with the "complexity" of the data collected as you describe....... References below are by no means comprehensive but a start ......

BLANCHET, F. G., P. LEGENDRE, R. MARANGER, D. MONTI, and P. PEPIN. 2011. Modelling the effect of directional spatial ecological processes at different scales. Oecologia 166: 357-368.

DRAY, S., P. LEGENDRE, and P. R. PERES-NETO. 2006. Spatial modelling: a comprehensive framework for principal coordinate analysis of neighbour matrices (PCNM). Ecological Modelling 196: 483-493.

LEGENDRE, P. 2008. Studying beta diversity: ecological variation partitioning by multiple regression and canonical analysis. Journal of Plant Ecology-Uk 1: 3-8.

LEGENDRE, P., X. MI, H. REN, K. MA, M. YU, I. F. SUN, and F. HE. 2009. Partitioning beta diversity in a subtropical broad-leaved forest of China. Ecology 90: 663-674.

PERES-NETO, P. R., and P. LEGENDRE. 2010. Estimating and controlling for spatial structure in the study of ecological communities. Global Ecology and Biogeography 19: 174-184.

STEGEN, J. C., and A. H. HURLBERT. 2011. Inferring Ecological Processes from Taxonomic, Phylogenetic and Functional Trait beta-Diversity. Plos One 6.


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Message: 2
Date: Mon, 7 May 2012 13:30:22 +0000 (UTC)
From: Ben Bolker <bbolker@gmail.com>
To: r-sig-mixed-models@r-project.org
Subject: Re: [R-sig-ME] request for help with glmm
Message-ID: <loom.20120507T152423-307@post.gmane.org>
Content-Type: text/plain; charset=utf-8

????? E?? <epitta@...> writes:

> 
> Hi,
> 
> I am a phd student in Greece. And I have some questions regarding the 
> use of glmm if the data include dissimilarity values.

> I do not know if this mailing list is appropriate for my questions but 
> I do not know who else to turn to.

You might be better off with the r-sig-ecology mailing list,
where there will be more expertise on community ecology topics
such as beta diversity ...

> My data include islands in various archipelagos and presence-absence
> of species of 3 taxa on the them. I estimated beta diversity as
> compositional dissimilarity between pairs of islands in the same
> archipelago using the Jaccard coefficient (proportion of common
> species between two islands). For example if I have 5 islands in a
> given archipelago I end up with 10 dissimilarity values. I fitted a
> glmm model (using package lme4) to test for the effect of taxon and
> also the effect of inter-island distance, area and elevation
> differences between pairs of islands on beta diversity using
> archipelago as a random factor. However, dissimilarity values (and
> the rest) are not independent of each other in the same archipelago,
> because each island contributes to N - 1 of them. I read that a
> glmm allows for correlation between the observations of the same
> random factor. Does this mean that a glmm takes into account the
> fact that the dissimilarity values are not independent from each
> other? Or should I somehow take into account the fact that
> dissimilarity values in the same archipelago are not independent of
> each other.

This is a little bit tricky. You *might* be able to do this
by using 'island identity' as a random factor as well, but it's
also quite possible that you would just run out of data that way.
People often use Mantel and partial Mantel tests to do inference
on these kinds of pairwise comparisons (i.e. use randomization
to compare the matrix of pairwise area differences with the matrix
of pairwise compositional dissimilarities). It's certainly
the case that the model you've set up so far does *not* account
for the correlation due to island identity.

Ben Bolker



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