[R-sig-eco] How to incorporate spatial autocorrelation in multivariate GLM

[Tim Meehan]

Hi Alexandre,


Not sure what the best solution is, but a few hacker ideas come to
mind.  First,
you could create a spatially lagged variable from scratch.  This would be
created by deciding on a neighborhood size, say first order neighbors, and
then creating a variable that was the average response (Y) value for the
first order neighbors.  Neighborhood size could be guestimated by looking
at residual maps.  This is similar to what happens in simultaneous
autoregressive (SAR) lagged models. Then this lagged variable could be a
fixed covariate in your model.  You could test residuals from the lagged
model to see if this removed your spatial autocorrelation.


Since you mentioned a GAM approach, you could also do a spatial GAM, where
Lat and Long variables are specified as smooth covariates with lots of
knots to account for short range spatial structure. Again, you could test
your residuals to see if this removed your spatial autocorrelation.


If you are comfortable with Bayesian modeling, Banerjee et al. (2015,
‘Hierarchical modeling and analysis for spatial data’) have a chapter on
multivariate spatial modeling, with a brief mention of generalized linear
models.


Some food for thought.


Best,

Tim

On Wed, Sep 9, 2015 at 6:25 AM, Alexandre F. Souza <
alexsouza.cb.ufrn.br at gmail.com> wrote:

> Dear friends,
>
> I would like to ask for some advice.
>
> I am embarking in the analysis of species occurrence date across
> biogeographic scales in South America. I am willing to try to jump from
> more traditional distance-based multivariate analysis (e.g., RDA on
> hellinger-transformed abundance data) to multivariate GLM as proposed by
> Warton (mvabund package) and also by Yee (VGAM package).
>
> However, distance-based methods have grown to incorporate spatial
> dependency through the development of MEM and AEM techniques, which model
> symmetric and asymmetric spatial relationships and can be included in the
> explanatory side of the analysis.
>
> Reading the multivariate GLM papers, however, I have not seen clear mention
> on how to control or include spatial autocorrelation. I am thinking of
> including MEM and perhaps AEM variables simply as co-variables added to the
> explanatory environmental variables in the multivariate GLM.
>
> Is this a step I will regret later on?
>
> Thanks in advance for any thoughts,
>
> All the best,
>
> Alexandre
>
> --
> Dr. Alexandre F. Souza
> Professor Adjunto III
> Universidade Federal do Rio Grande do Norte
> CB, Departamento de Ecologia
> Campus Universitário - Lagoa Nova
> 59072-970 - Natal, RN - Brasil
> lattes: lattes.cnpq.br/7844758818522706
> http://www.docente.ufrn.br/alexsouza
>
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