Can regression and IDW spatial interpolation be done in one model in R? -

i spatial modelling of variable t (temperature). use commonly used in literature - perform regression (using variables altitude etc.) , spatially interpolate residuals using idw. r package gstat seems have option:

interpolated <- idw(t ~ altitude, stations, grid, idp=6) spplot(interpolated["var1.pred"]) 

but in documentation of idw() write:

function idw performs [...] . don't use predictors in formula.

and actually, result looks if regression performed, without spatial interpolation of residuals. know can manually:

m1 <- lm(t ~ altitude, data = data.frame(stations)) tres <- resid(m1) res.int <- idw(tres ~ 1, stations, grid, idp=6) tpred <- predict.lm(m1, grid) spplot(spatialgriddataframe(grid, data.frame(t = tpred + data.frame(res.int)['var1.pred']))) 

but have many drawbacks - model not in 1 object, cannot directly summary, check deviance, residuals , importantly, crossvalidation... have done manually. so,

is there way how regression , idw in 1 model in r?

note don't want use different method of spatial interpolation, because idw used in area of modelling , tested these purposes.

so want regression first, , perform idw on residuals. cannot done in 1 go, both theoretical , software point of view:

• theoretical, kriging presents unified way of treating both model , residuals in 1 go using linear model , create prediction, i.e. linear regression spatially correlated residuals. in case of hybrid model, theoretical frame not present. because of ad hoc nature not recommend doing this.
• practically, gstat not support doing in 1 go.

i'd recommend going kriging, established , published method. if has not been used in area of expertise, time introduce it. have @ tps function in fields package.

some years wrote a technical report dutch meteorological office might of interest you, deals interpolation of evaporation.