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

Ken Nussear knussear at usgs.gov
Thu Nov 8 22:47:55 CET 2007

```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)
 0.9934701

> cor(fitted.likGRF(m2, spatial=FALSE), td\$Crotaphytus)
 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

```