A Bayesian approach to spatial correlations in the multivariate probit model

Ordered categorical data arise in many applied settings. For example, many surveys have responses that may be restricted to “Strongly Disagree”, “Disagree, “Neutral”, “Agree”, and “Strongly Agree”. Here, the responses are ordinal variables. That is, the agreeability of respondents to questions have relative ranks, but there is no measure of exact magnitude like there is with continuous variables. In many scenarios, questions may have correlated responses. As well, different respondents may be spatially or otherwise correlated. Probit models are a means to using normal latent variables in modelling ordinal responses. In this project, we take a Bayesian approach and include both “between question” and “between respondent” correlations in a multivariate probit model. We discuss the efficacy of this spatial multivariate probit model.