Dear Klaus,

there's broadly 2 approaches; one builds on the so-called model-based 
geostatistics (MBG) approach by Diggle et al 1998 (and in the book by 
Ribeiro and Diggle), the other uses Pearson residual variogram and 
covariance matrices that use the variance function for the mean 
dependent (co)variances. I have some experience with the latter, using 
count data, and published it in

E.J. Pebesma, R.N.M. Duin, P.A. Burrough, 2005. Mapping Sea Bird 
Densities over the North Sea: Spatially Aggregated Estimates and 
Temporal Changes. Environmetrics 16 
<http://www3.interscience.wiley.com/cgi-bin/jissue/110577560>, (6), p 
573-587 <http://dx.doi.org/10.1002/env.723>.

Here, counts depend on distance to the coast and water depth.

The funny thing in this approach (not mentioned e.g. by Waller & Gotway) 
that kriging predictions may be outside of the possible observation 
range, negative counts or predictions outside 0/1 in the binary case. 
There's some infrastructure in package gstat to do this.

MBG does not have this problem, but needs MCMC where checking of 
convergence issues and a lot of patience is needed.
--
Edzer

Klaus Ecker wrote:
> Hello
>
> I want to incorporate an external trend when 
> interpolating binary data (presence absence data 
> from vegetation records). To my understanding 
> universal kriging does not work with binary 
> response data and does not apply generalized 
> linear models for the covariates. Does geoRglm provide these opportunities?
>
> Kriging residuals from a deterministic model 
> (regression kriging) would allow for logistic 
> regression models to be used for the trend. 
> However, applications of regression kriging in 
> ecology are rare, especially in recent years. Is there anything wrong about it?
>
> With logistic regression the variogramm is 
> commonly calculated on standardised (Pearson) 
> residuals. But I have never seen how to back 
> transform them before they are added to the 
> logistic trend model. Is it correct to multiply 
> the kriging predictions by the square root of the 
> variance of the response residuals?
>
> Many thanks
>
> Klaus
>
>
>
>
>
> ______________________________________________
>
>
> Klaus Ecker
> Swiss Federal Research Institute WSL
> Biodiversity and Conservation Biology
> Spatial Ecology
> Zürcherstrasse 111
> CH-8903 Birmensdorf (SWITZERLAND)
>
> phone: +41-44-7392-378
> fax: +41-44-7392-215
> e-mail: klaus.ecker@wsl.ch
> internet: http://www.wsl.ch
>
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