Spatial Regression Models for Areal Data Analysis

The primary models of interest for areal data analysis are regression models. In the same way that geo-regression models were used to study relations among continuous-data attributes of selected point locations (such as the California rainfall example), the present spatial regression models are designed to study relations among attributes of areal units (such as the English Mortality example in Section 1.3 above). The key difference is of course the underlying spatial structure of this data. In the case of geo-regression, the fundamental spatial assumption was in terms covariance stationarity, which together with multi-normality, enabled the full distribution of spatial residuals to be modeled by mean of variograms and their associated covariograms. In the present case, this stationarity assumption is replaced by spatial autogressive hypotheses that are based on specific choices of spatial weights matrices, as developed in Section 5. Here we start with the most fundamental spatial autogressive hypothesis in terms of regression residuals themselves.