SAR: Spatial Auto-Regression

Project for Applied Statistics

Using R (2.6.2)

Linear regression is among the most used techniques in statistics. Nevertheless, when it is used on a spatially distributed dataset, the resulting model is neglecting all information relative to the spatial correlation in the observations and its predictive power is sub-optimal. In particular, the regression error is spatially auto-correlated and the fundamental hypothesis that errors are independent is not satisfied.

SAR implements a sub-model for the regression error by means of a distance matrix for which estimation $n^3$ operations are required. This high order complexity is reduced by observing that spatial correlation vanishes as the observations distance increases, allowing to neglect the contribution of most observations for each data entry considering exclusively contributions from the nearest $m$ observations.