Thanks for those suggestions, but unfortunately, these approaches seem to be
largely outside my skills.

Arnaud

2011/1/17 Douglas Bates <bates@stat.wisc.edu>

> On Mon, Jan 17, 2011 at 8:33 AM, Ben Bolker <bbolker@gmail.com> wrote:
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> > On 11-01-17 09:03 AM, Arnaud Mosnier wrote:
> >> Dear list,
> >>
> >> Is there a way in R to do a mixed logistic regression with a spatial
> >> autocorrelation structure ?
> >>
> >
> >  The only straightforward solution I know of is via glmmPQL (MASS
> > package), although you should be careful (e.g. try fitting to simulated
> > data where you know the answer first) because penalized quasi-likelihood
> > is biased for binary data.
>
> As in previous discussions of modeling marginal variance-covariance
> structures (as in adding spatial correlation) for the response in a
> generalized linear mixed model, I think it is best to consider the
> model carefully to ensure that it is sensible.
>
> For a linear model where the distribution of the response is
> multivariate Gaussian or for a linear mixed model where the
> conditional distribution of the response, given the random effects, is
> multivariate Gaussian, it is possible to model the variance-covariance
> of this distribution separately from the model for the mean.  In the
> case of a logistic GLM or GLMM the only way that I know how to make
> sense of the model is that the distribution of the response (for known
> values of the parameter) or the marginal distribution of the response,
> given the random effects and model parameters, is a vector of
> independent Bernoulli or binomial distributions.
>
> Because the iterative scheme for determining the parameter estimates
> in a GLM (or the conditional parameter estimates and the modes of the
> random effects in a GLMM) is based on a weighted least squares
> calculation, it is sometimes assumed that this can be converted to a
> generalized least squares calculation.  You can certainly do this but
> it doesn't reflect a model that I can describe.
>
> It may be that I don't know enough about generalized linear models to
> understand how one would incorporate spatial correlation in such a
> model but I am somewhat suspicious of the practice.  In discussing
> this with Jun Zhu, our local expert on spatial statistics, she
> suggested that a preferred practice is to build the spatial
> correlation into the distribution of the random effects, say by having
> one random effect per location, and that would make sense to me
> because the marginal distribution of the random effects is
> multivariate Gaussian.
>
> >   One of the generalized estimating equation packages (geepack, etc.)
> > may also work.  If you have only spatial autocorrelation (i.e. no random
> > block effects) then the geoRglm and spatcounts packages may also be of
> use.
> >
> >  Ben Bolker
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