A Bayesian Probit Model With Spatial Dependencies

Abstract

A Bayesian probit model with individual effects that exhibit spatial dependencies is set forth. Since probit models are often used to explain variation in individual choices, these models may well exhibit spatial interaction effects due to the varying spatial location of the decision makers. That is, individuals located at similar points in space may tend to exhibit similar choice behavior. The model proposed here allows for a parameter vector of spatial interaction effects that takes the form of a spatial autoregression. This model extends the class of Bayesian spatial logit/probit models presented in LeSage (2000) and relies on a hierachical construct that we estimate via Markov Chain Monte Carlo methods. We illustrate the model by applying it to the 1996 presidential election results for 3,110 US counties.

Knowledge Spillovers Across Europe: Evidence from a Poisson Spatial Interaction Model with Spatial Effects

“…which as noted in Smith and LeSage (2004) is not reducible to a standard distribution. We rely on the univariate numerical integration approach described in Smith and LeSage (2004) to sample from these two conditional posterior distributions.…”

“…In this appendix we follow Smith and LeSage (2004), and derive a sequence of univariate conditional posterior distributions for each component of θ and φ that allows the MCMC sampling scheme to be applied to models involving large numbers of regions n while avoiding matrix inversion of the n-by-n matrices required for the multivariate normals set forth in the text of the paper. For small problems involving n < 100 regions, it is probably faster to simply carry out the matrix inversions, but no experiments have been carried out to assess the relative computational trade-offs here.…”

“…We rely on the univariate numerical integration approach described in Smith and LeSage (2004) to sample from these two conditional posterior distributions. Specifically, we rely on a vectorised expression: …”

A latent variable representation of count data models to accommodate spatial and temporal dependence: Application to predicting crash frequency at intersections

“…We now add an index t for time period (t = 1, 2, …, T). Many studies attempt to side-step the high dimensional problem by clustering observation units into "regions", and then considering a spatial error dependency over the regions rather than the observational units (see LeSage, 2004 andPalmquist, 2003). parameter, qt x is a (L×1)-vector of exogenous variables (including a constant now to accommodate time-stationary random effects through a random coefficient on this constant) and q β is an observation unit-specific (L×1)-vector of coefficients assumed to be a realization from a multivariate normal distribution with mean vector b and covariance…”

Application of Dynamic Spatial Ordered Probit Model

“…In short, a dynamic ordered probit model with spatial and temporal autocorrelation can be described by extending existing specifications of spatial probit models, static and dynamic, ordered and categorical. The most closely related works are those by , Wang and Kockelman (2008), Smith and LeSage (2004) and Girard and Parent (2001).…”