Residual mapping and spatial autocorrelation. SAR model.

Dear list members!

To map residuals from a single linear regression model which is based on high 
resolution raster data (cellsize 5m, approx. n=290000), i try to take into 
account for spatial autocorrelation in the residuals. Several morphometric 
layers (e.g. slope, solar potential, elevation etc.) serve as predictors in 
order to explain surface elevation changes of a glacier surface.

By using SAR model with spatial weights (neighbor list object with 3,984 
neighbors per observation in average) which were generated based on the

current predictor, a very efficient fit results. Hence, the residual map 
shows small values almost across the whole surface. The same model with each 
of the other predictors leads to almost the same fit and a similar residual 
map.

The problem is, that if i take the autocorrelation into account and model 
with SAR, i cannot identify spatial patterns of the quality of the fit in 
relation to different predictors. If i model with OLS, i get sensible 
variations between the different residual maps, but the residuals are 
strongly autocorrelated as this is natural for high resolution raster data.

- Do you have any ideas about an other approach for defining spatial weights?

- Are there any legitimations for ignoring the autocorrelated residuals of 
the OLS model since the research objective is to derive sensible variations 
in the residual maps?

### selected code for calculating spatial weights and performing SAR: ###

library(gstat)
library(sp)
library(spdep)
library(rgdal)

dst <- max(slot(slot(elev, "grid"), "cellsize"))
elev_nb <- dnearneigh(coordinates(elev), 0, dst)
sp_weights <- nb2listw(elev_nb)

dif_vec <- c(dif at data$band1)
elev_vec <- c(elev at data$band1)

sp_fit <-  spautolm(dif_vec~slope_vec, listw = sp_weights, family="SAR", 
method="Matrix", na.action=na.exclude)

#################

system: linux high performance cluster node with 2 Intel Quad-Core L5420 CPUs 
(8 cores running on 2.5 GHz), 32 GB DDR2 RAM (4 GB per core)
R version 2.13

Thank you very much in advance!

Max