Spatially Autoregressive Models

Spatial autoregressive models differ from standard regression models by having the response variable Y, on both sides of the equal sign, in order to account for within variable correlation. The right-hand term containing Y comprises values for other observations, with the adjective spatial indicating that these other values are selected according to the geographic nearness of their locations to that of a given observation. In other words, spatial autocorrelation is being accounted for. These regression equations furnish descriptions of frequency distributions that become distorted from their conventional shapes by increasingly stronger positive spatial autocorrelation, the most prevalent situation. The bell-shaped curve becomes flattened, Poisson distribution skewness and outliers increase, and the binomial distribution becomes increasingly dichotomous in nature. These regression equations can be specified, and their parameters estimated, for normal, Poisson, and binomial probability models, but not with standard statistical software package routines. The most common and easiest implementation is for the auto-normal specification, with the conditional, simultaneous, and lag versions being the widely popular ones. Two of the most pressing unresolved issues are statistical distribution theory to test for residual spatial autocorrelation, and computer software to implement Markov chain Monte Carlo estimation techniques for auto-Poisson and auto-binomial specifications.