Double Generalized Spatial Econometric Models

Abstract

The authors offer a unified method extending traditional spatial dependence with normally distributed error terms to a new class of spatial models based on the biparametric exponential family of distributions. Joint modeling of the mean and variance (or precision) parameters is proposed in this family of distributions, including spatial correlation. The proposed models are applied for analyzing Colombian land concentration, assuming that the variable of interest follows normal, gamma, and beta distributions. In all cases, the models were fitted using Bayesian methodology with the Markov Chain Monte Carlo (MCMC) algorithm for sampling from joint posterior distribution of the model parameters.

Conditional overdispersed models: Application to count area data

“…This specific issue is addressed by proposing the use of a so-called weight matrix in the model, where its parameter estimates are associated to the corresponding lag variable modeling this neighborhood association. 17,19 Therefore, in the proposed models, on the one hand, a new parameter quantifies the spatial association explained by the considered neighborhood structures, and, on the other hand, the overdispersion parameter quantifies the heteroscedasticity and spatial dependence that is not explained by the spatial structures incorporated into the model.…”

“…15 Therefore, taking into account the existing spatial association between observations on the variable under study, among other factors or variables that may be sources of overdispersion, is very relevant in the statistical analysis of this type of data. 16 Along these lines, being able to determine the levels of spatial association in count area data is fundamental to both specify and understand, for example, how a given illness or epidemic develops in a given area, 12 how one can better understand the concentration of land phenomenon, 17 or how variables and which variables affect the extinction of given endangered species. 18 In these cases, the larger the association, the more disseminated the phenomenon under study will be.…”