Estimating spatial weighting matrices in cross-regressive models by entropy techniques

The traditional approach to estimate spatial models bases on a preconceived spatial weights matrix to measure spatial interaction among locations. The a priori assumptions used to define this matrix are supposed to be in line with the "true" spatial relationships among the locations of the dataset. Another possibility consists on using some information present on the sample data to specify an empirical matrix of spatial weights. In this paper we propose to estimate spatial cross-regressive models by generalized maximum entropy (GME). This technique allows combing assumptions about the spatial interconnections among the locations studied with information from the sample data. Hence, the spatial component of the model estimated by the techniques proposed is not just preconceived but it allows incorporating empirical information. We compare some traditional methodologies with the proposed GME estimator by means of Monte Carlo simulations in several scenarios and show that the entropy-based estimation techniques can outperform traditional approaches. An empirical case is also studied in order to illustrate the implementation of the proposed techniques for a real-world example.