Generalization of regression analysis to the spatial context

Our day-to-day experience suggests that certain variables are local in their effects. The influence of such variables is limited within the boundaries of the spatial entity (district) where they are physically located. In contrast, the effects of some other variables are percolating or pervasive in nature. They permeate through the district boundaries or sometimes grossly transcend the local borders. The intensity of influence of such variable often decreases with an increase in the distance traversed, although the rate of such decay may be slow or rapid. Therefore, the value of the dependent variable observed in the one district may be influenced by the value of an explanatory variable in the other district. In the spatial context, therefore, contiguity (interactivity or connectedness) is very important. In the real world, ‘connectedness’ (interactivity or contiguity) is not a simple binary relationship that may capture the openness of the spatial entities to each other. One may discriminate among the instances of ‘interactivity’ or ‘connectedness’ arising due to common vertex and common boundary segments of different magnitudes. There can be several other criteria to measure ‘interactivity’ or ‘connectedness.’ Conventionally variance is visualized as the expectation of (squared) deviations of the individual variate values from the mean value of the variate. Similarly, covariance (of any two variates) is visualized as the expectation of the product of deviations of the variates concerned from their respective mean values. However, variance may also be considered as the expectation of squared deviations of each individual observation from the other individual observations rather than from its own mean. Covariance also may be viewed analogously. This view provides a basis to generalize the conventional regression analysis to the spatial context. A Fortran computer program is also provided.