[R] analyzing binomial data with spatially correlated errors

[Ben Bolker]

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Douglas Bates wrote:
| On Wed, Mar 19, 2008 at 3:02 PM, Ben Bolker <bolker at ufl.edu> wrote:
|> Jean-Baptiste Ferdy <Jean-Baptiste.Ferdy <at> univ-montp2.fr> writes:
|>
|>  >
|>  > Dear R users,
|>  >
|>  > I want to explain binomial data by a serie of fixed effects. My
problem is
|>  > that my binomial data  are spatially correlated. Naively, I
thought I could
|>  > found something similar to gls to analyze such data. After some
reading, I
|>  > decided that lmer is probably to tool I need. The model I want to
fit would
|>  > look like
|>  >
|>  > lmer ( cbind(n.success,n.failure) ~ (x1 + x2 + ... + xn)^2 ,
family=binomial,
|>  > correlation=corExp(1,form=~longitude+latitude))
|>  >

| This is more than a notational difference.  In a linear model the
| effect of b is limited to the linear predictor and, through that, the
| mean.  The variance-covariance specification can be separated from the
| mean and, hence, can be specified separately.  It is easy to fool
| yourself into thinking that the same should be true for generalized
| linear models, just like it is easy to fool yourself into thinking
| that all the arguments for the lme function will work unchanged in
| lmer.

~  Fair enough.  I guess the model I was thinking of was

~  Y ~ Binomial(p,N)
~  logit(p) ~ MVN(mu,Sigma)
~  mu = (determined by model matrix and predictors)
~  Sigma = (exponential spatial correlation matrix)*sigma^2

~ This model is certainly different from the model that the original
poster may have been thinking of, because in the limit where there
is no extra-binomial variation, there can't be any correlation either.
On the other hand, it seems to be a sensible model.

~  cheers
~    Ben Bolker

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