Comparison of Performance of REML and OLS Variogram Fitting on Simulated Data.

Geostatistics plays a very important role in the field of soil mapping and characterization. Obtaining experimental variograms from collected data and fitting them with permissible variogram models is one of the central tasks in data interpolation by geostatistical tools. The objective of this study is to compare performances of two commonly used methods of variogram fitting: Ordinary Least Squares (OLS) and Restricted Maximum Likelihood (REML) in several simulated datasets with diverse characteristics. Simulated data sets were created so as to represent a diverse range of local spatial variations described by variograms of different shapes, linear trends of varying strengths, and normally distributed noises of different magnitudes. Effects of sample size and data configuration on the performance of variogram fitting methods were also examined. Analysis was performed in SAS 9.1. Results indicate that in majority of samples OLS performed substantially better than REML, because not only average of OLS estimations was closer to the line of original variogram model but also standard deviation of the method estimations was smaller than REML one. Both OLS and REML underestimated the range of the original variogram model, but range value for OLS was bigger, meaning that it is able to recognize existing spatial dependence between the points at a longer distance.