Capturing Patterns of Spatial and Temporal Autocorrelation in Ordered Response Data , Using a Bayesian Approach : A

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 is found that the DSOP model yields much more accurate estimates than standard, non-spatial techniques. As for model selection, the DSOP model is clearly preferred to standard OP, dynamic OP and spatial OP models. These methods are then used to analyze land use changes over an 18-year period in Austin, Texas. In this analysis, temporal and spatial autocorrelation effects are found to be significantly positive. In addition, increases in travel times to the region’s central business district (CBD) are estimated to substantially reduce land development intensity. 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 twodimensional autocorrelation.