On the Akaike Information Criterion for choosing models for variograms of soil properties

A problem in the application of geostatistics to soil is to find satisfactory models for variograms of soil properties. It is usually solved by fitting plausible models to the sample variogram by weighted least squares approximation. The residual sum of squares can always be diminished, and the fit improved in that sense, by adding parameters to the model. A satisfactory compromise between goodness of fit and parsimony can be achieved by applying the Akaike Information Criterion (AIC). For a given set of data the variable part of the AIC is estimated by where n is the number of experimental points on the variogram, R is the residual sum of squares and p is the number of parameters in the model. The model to choose is the one for which  is least.
The AIC is closely related to Akaike's earlier final prediction error and the Schwarz criterion. It is also equivalent to an F test when adding parameters in nested models.