Simulating Spatial Auto-Regressions (SAR) on Random Points

Spatial Auto-Regressive (SAR) models for point data Zi=g(Zj;Xi,Yi), where Xi,Yi are planar coordinates (e.g. longitude and latitude) are useful for spatial interpolation and prediction. In vector form, these models are representable as Z=a+b*Wm*Z+c*Wm*Y+E , where Wm is the contiguity matrix of order m, where m>0 is the number of spatial lags, or contiguous terms Zi-k. This program computes the matrices Wm by following the Multidirectional principle of nearest-neighbors (NN) and the Unidirectional approach of north-south NN, after sorting the data by latitude. Further, the matrices Wm are computed either in binary form (0,1) or with 1 replaced by the inverse distance (ID) of the points; in both cases, when combined in a single matrix, they must be normalized by row. The second goal of the program is to evaluate by simulation experiments the statistical performance (with relative bias and mean squared error) of least square (LS), maximum likelihood (ML) and generalized moments (GM) estimators, under various conditions. The SAR processes are generated in reduced form as Z=inv(I-b*Wm)*(a+c*Wn*Y+E) and the ML, GM estimates are computed with the Spatial Econometric Toolbox of LeSage and Pace. The scripts of simulations also provide LS parameter estimators for various SAR models which involve the matrices Wm. A SARp_demo script is also provided which runs interactively.