Bayesian Spatial Modeling for Housing Data in South Africa

Spatial process models are being increasingly employed for analyzing data available at geocoded locations. In this article, we build a hierarchical framework with multivariate spatial processes, where the outcomes are "mixed" in the sense that some may be continuous, some binary and others may be counts. The underlying idea is to build a joint model by hierarchically building conditional distributions with different spatial processes embedded in each conditional distribution. The idea is simple and the resulting models can be fitted to multivariate spatial data using straightforward Bayesian computing methods such as Markov chain Monte Carlo methods. Bayesian inference is carried out for parameter estimation and spatial interpolation. The proposed models are illustrated using housing data collected in the Walmer district of Port Elizabeth, South Africa. Inferential interest resides in modeling spatial dependencies of dependent outcomes and associations accounting for independent explanatory variables. Comparisons across different models confirm that the selling price of a house in our data set is relatively better modeled by incorporating spatial processes.