# Re: [R] analyzing binomial data with spatially correlated errors

From: Ben Bolker <bolker_at_ufl.edu>
Date: Thu, 20 Mar 2008 10:08:51 -0400

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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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