Generalized spatial matrix specifications

In this article, we propose a model that generalizes some of the most popular choices in spatial linear modeling, such as the SAR and MESS models. Our idea builds on their representation as link functions applied to a spatial weight <i>W</i>, corresponding to the uniform and exponential distributions, respectively. By allowing for more general families of distribution functions, one can encompass both models and capture different spatial patterns. We provide some insights into the difference between specifications, with emphasis on advantages and shortcomings as well as on interpretation of the parameters and correspondences between models. By exploiting the possibility to obtain a formal power series representation of the link family, we define the quasi maximum likelihood estimator and study its asymptotic properties under Gaussian and non Gaussian errors. By applying our approach to data on 2000 US election participation, as in LeSage and Pace (2007), we show that this model is able to capture a finite order neighboring spillover structure, as opposed to the infinite order implied by both the SAR and MESS models.