A clipped latent variable model for spatially correlated ordered categorical data

We propose a model for a point-referenced spatially correlated ordered categorical response and methodology for inference. Models and methods for spatially correlated continuous response data are widespread, but models for spatially correlated categorical data, and especially ordered multi-category data, are less developed. Bayesian models and methodology have been proposed for the analysis of independent and clustered ordered categorical data, and also for binary and count point-referenced spatial data. We combine and extend these methods to describe a Bayesian model for point-referenced (as opposed to lattice) spatially correlated ordered categorical data. We include simulation results and show that our model offers superior predictive performance as compared to a non-spatial cumulative probit model and a more standard Bayesian generalized linear spatial model. We demonstrate the usefulness of our model in a real-world example to predict ordered categories describing stream health within the state of Maryland.