Baysian Inference for Ordered Response Data with a Dynamic Spatial Ordered Probit Model

Many databases involve ordered discrete responses in a temporal and spatial context, including, for example, land development intensity levels, vehicle ownership, and pavement conditions. An appreciation of such behaviors requires rigorous statistical methods, recognizing spatial effects and dynamic processes. This study develops a dynamic spatial ordered probit (DSOP) model in order to capture patterns of spatial and temporal autocorrelation in ordered categorical response data. This model is estimated in a Bayesian framework using Gibbs sampling and data augmentation, in order to generate all autocorrelated latent variables. It incorporates spatial effects in an ordered probit model by allowing for inter-regional spatial interactions and heteroskedasticity, along with random effects across regions or any clusters of observational units. The model assumes an autoregressive, AR(1), process across latent response values, thereby recognizing time-series dynamics in panel data sets. The model code and estimation approach is tested on simulated data sets, in order to reproduce known parameter values and provide insights into estimation performance, yielding much more accurate estimates than standard, non-spatial techniques. The proposed and tested DSOP model is felt to be a significant contribution to the field of spatial econometrics, where binary applications (for discrete response data) have been seen as the cutting edge. The Bayesian framework and Gibbs sampling techniques used here permit such complexity, in world of two-dimensional autocorrelation.