Probit Regression Model for Spatially Dependent Discrete Choice Data: A Simulation Study

This paper is about spatial econometrics in the context of discrete choice models for area data. It is presented here a simulation study of a (very useful) Bayesian econometric model for the probit regression in binary responses with spatially structured random effects in the latent variable.Because of the large number of parameters to be estimated by stochastic simulation and the model complexity itself, in some cases it is not certain the convergence in the Gibbs sampling procedure. With this respect, it is proposed in this paper some modification in the MCMC procedure in order to improve convergence. Also a couple of particular cases of this spatial model, which are more known in the literature, are included in the analysis as reference for comparison.The simulation study considers the spatial structure of the geographical (administrative) region of Campinas, SP, Brazil, composed by 90 counties. The model is simulated according to different settings, with three distinct sample sizes, varying the number of agents in each region, where are generated 150 samples at each area. Also, it is considered six different values for the spatial parameter. In all settings, it is compared the estimation performance of the proposed procedure with the references in the econometric literature and the results are discussed. Also, a short illustration of the main procedures considered is presented involving real data about the 2002 Brazilian presidential election.