[R-sig-Geo] question about fitted values form geoR - results 'too good'

[Ken Nussear]

Hi

I'm using geoR for some spatial linear models and I'm getting  
surprisingly optimistic values from the spatial models relative to the  
non-spatial, even when the models appear to be performing about  
equally (by AIC comparison)

For example

This model relating encounter rates of lizards to a soil substrate  
parameter gives

> > summary(m2)
> Summary of the parameter estimation
> -----------------------------------
> Estimation method: maximum likelihood
>
> Parameters of the mean component (trend):
>  beta0  beta1
> 0.0312 0.0024
>
> Parameters of the spatial component:
>    correlation function: exponential
>       (estimated) variance parameter sigmasq (partial sill) =  0.0082
>       (estimated) cor. fct. parameter phi (range parameter)  =  797.1
>    anisotropy parameters:
>       (fixed) anisotropy angle = 0  ( 0 degrees )
>       (fixed) anisotropy ratio = 1
>
> Parameter of the error component:
>       (estimated) nugget =  0.002
>
> Transformation parameter:
>       (fixed) Box-Cox parameter = 1 (no transformation)
>
> Maximised Likelihood:
>    log.L n.params      AIC      BIC
>  "53.44"      "5" "-96.87" "-86.57"
>
> non spatial model:
>    log.L n.params      AIC      BIC
>  "51.99"      "3" "-97.98"  "-91.8"


With a difference in AIC of only about 1.

However looking at the predicted values versus the fits for the model  
The spatial model fitted values appear to be some how too good.

 > cor(fitted.likGRF(m2, spatial=TRUE), td$Crotaphytus)
[1] 0.9934701


 > cor(fitted.likGRF(m2, spatial=FALSE), td$Crotaphytus)
[1] 0.2522837

So I don't get how the spatial model with only a delta AIC of 1 can  
have a correlation with the dependent variable that is this high. Am I  
mis-interpreting the values I'm getting from the fitted call, or is  
something amis.  I've tried this with different data sets and I'm  
getting the same result.

Thanks

Ken