page_title: Regression-kriging
section_title: Software to run regression-kriging
hierarchical_section_title: Regression-kriging / Software to run regression-kriging
caption_attribution_description: English: After Hengl et al. (2004; Geoderma)
context_page_description: In applied statistics, regression-kriging is a spatial prediction technique that combines a regression of the dependent variable on auxiliary variables with kriging of the regression residuals. It is mathematically equivalent to the interpolation method variously called universal kriging and kriging with external drift, where auxiliary predictors are used directly to solve the kriging weights.
context_section_description: Regression-kriging can be automated e.g. in R statistical computing environment, by using gstat and/or geoR package. Typical inputs/outputs include:
  INPUTS:
  Interpolation set (point map) —   at primary locations;
  Minimum and maximum expected values and measurement precision ();
  Continuous predictors (raster map) — ; at new unvisited locations
  Discrete predictors (polygon map);
  Validation set (point map) —   (optional);
  Lag spacing and limiting distance (required to fit the variogram);
  OUTPUTS:  	
  Map of predictions and relative prediction error;
  Best subset of predictors and correlation significance (adjusted R-square);
  Variogram model parameters (e.g. , , )
  GLS drift model coefficients;
  Accuracy of prediction at validation points: mean prediction error (MPE) and root mean square prediction error (RMSPE);
caption: Example of a generic framework for spatial prediction of soil variables based on regression-kriging.[9]
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