# Validation of Regression Kriging

I am interested in exploring the idea of generating a predictive model for a target variable in a spatial context. I would then like to correct the residuals of this model using kriging, i.e. in a nutshell you sum up the results from both models and take that as the final prediction: The classical approach is to fit a GLM and then krige (is that how you turn it into a verb?) its residuals. I would like to fit something like a Random Forest. Which leads me to my question. How do you validate these models? If I wanted to do cross-validation do I separate the data (e.g. 10-folds) and reapeatedly fit the model, krige the corresponding residuals -> predict on test set, etc. Or do I have to separate the data into 3 sets, one to fit the model, see how it predicts on another data set, krige THOSE errors and then test on the final data set, repeat. What is the usual apporach to do this correctly?

Thank you in advanced.

I'm using R by the way.

• The usual way this is done is with "universal kriging." That fits easily within the geostatistical GLM simply by including the covariates: in effect, the "residuals" (which don't even make sense for most non-Gaussian GLMs, by the way) are "corrected" at the same time the trend is fit. Because that's really just another (linear) model, you can validate it the same way you would validate any model. – whuber Jun 14 '13 at 17:38
• I have been reading this document: Investigating the potentiality of Regression Kriging in the Estimation of Soil Prganic Carbon Versus the Extracted Result from the Existing Soil Map. By Navneet Kumar. There he explains the difference between Regression kriging, Kriging tiwh external drift and Universal kriging: UK and KED compute trend along with residuals simultaneously in one system and gives a combined kriging variance whereas in regression kriging the trend is first subtracted from the residuals, krige the residuals separately and finally add trend back... – JEquihua Jun 14 '13 at 18:03
• Regression kriging was popular in the 1980's, but was found to be a biased estimator and quickly vanished by the early 1990's. It's still attractive for its intuitive decomposition of the problem and simple implementation, but you should be wary of it. BTW, the "regression kriging" I am thinking of fits the trend using generalized least squares (obtaining the covariances from the variogram, of course) and then iterates, re-estimating the covariances from the new residuals, until approximate convergence (which is very rapid). – whuber Jun 14 '13 at 19:15
• How does Random Forests fit into your question? You can spatially constrain a RF model by including a distance matrix (see Evans et al., 2011 in Predictive Modeling in Landscape Ecology). – Jeffrey Evans Jun 14 '13 at 19:44
• I recently took a workshop where the professor (Gerard Heuvelink) and he mentioned that regression kriging could be based on any predictive model, he specifically mentioned random forests. I was just curious about this comment and wanted to try it out but I am still confused on to how to validate this type of exercise. @Whuber I am not sure what regression kriging you are thinking about, I am talking about the one defined in wikipedia: Regression-kriging is implementation of the best unbiased linear predictor for spatial data. At the same conference I saw it being used extensively. – JEquihua Jun 15 '13 at 20:35