Regression kriging pre-work reading
In the previous pages we looked at a few soil spatial prediction functions which at the most fundamental level, target the the correlation between the target soil variable and the available covariate information.
We fitted a number of models which included simple linear functions to non-linear functions such as regression trees to other more complicated data mining techniques e.g. Cubist and Random Forest).
In this section we will extend upon this DSM approach from what are called deterministic models to also include the spatially correlated residuals that result from fitting these models.
The approach we will now concentrate is a hybrid approach to modelling, where the predictions of the target variable are made via a deterministic method (regression model with covariate information) and a stochastic method where we determine the spatial auto-correlation of the model residuals with a variogram.
The deterministic model essentially detrends the data, leaving behind the residuals for which we need to investigate whether there is additional spatial structure which could be added to the regression model predictions.
These residuals are the random component of the scorpan + e model. This method is described as regression kriging and has formally been described in Odeh et al. (1995) and is synonymous with universal kriging (Hengl et al. 2007), which is the formal linear model procedure to this soil spatial modeling approach.
The purpose of this exercise is to introduce some basic concepts of regression kriging. You will have already had some experience in regression models. We have also investigated briefly the fundamental concepts of kriging for which the variogram is fundamental to help in understanding about the spatial behavior of soil materials.
References
Hengl, T, G. B. M Heuvelink, and D. G Rossiter. 2007. “About Regression Kriging: From Equations to Case Studies.” Computers & Geosciences 33: 1301–15.
Odeh, I. O. A, A. B McBratney, and D. J Chittleborough. 1995. “Further Results on Prediction of Soil Properties from Terrain Attributes: Heterotopic Co-Kriging and Regression Kriging.” Geoderma 67: 215–26.