Abstract
In this article we present the Bayesian estimation of spatial probit models in R and provide an implementation in the package spatialprobit. We show that large probit models can be estimated with sparse matrix representations and Gibbs sampling of a truncated multivariate normal distribution with the precision matrix. We present three examples and point to ways to achieve further performance gains through parallelization of the Markov Chain Monte Carlo approach.
Highlights
While all of these packages deal with linear spatial models, in this article we focus on a nonlinear model, the spatial probit model, and present the Bayesian estimation first proposed by LeSage (2000)
In this article we presented the estimation of spatial probit models in R and pointed to the critical implementation issues
Our performance studies showed that even large problems with n = 10, 000 or n = 100, 000 observations can be handled within reasonable time
Summary
The abundance of geolocation data and social network data has lead to a growing interest in spatial econometric methods, which model a contemporaneous dependence structure using neighboring observations (e.g. friends in social networks). GMM is massively more efficient computationally than Bayesian Markov Chain Monte Carlo (MCMC), as a instrumental-variables estimation it will work well only in very large samples This point is brought by Franzese et al (2013), who compares different spatial probit estimation strategies. See for example Albert (2007) and the accompanying package LearnBayes for an introduction to Bayesian statistics in R (Albert, 2012) This sampling for the posterior distribution p(z, β, ρ|y) can be realized by a Markov Chain Monte Carlo and Gibbs sampling scheme, where we sample from the following three conditional densities p(z|β, ρ, y), p(β|z, ρ, y) and p(ρ|z, β, y): 1.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
