Dynamic Cumulative Probit Models for Ordinal Panel-Data; a Bayesian Analysis by Gibbs Sampling

This paper deals with a dynamic version of the cumulative probit model. A general multivariate autoregressive structure is proposed for modeling the temporal dynamic of both regression and threshold parameters. Conjugate and diffuse prior distributions are used for the variances of the (normally distributed) transition error terms. Introducing latent variables for each ordered categorical observation, statistical inference is done by means of the Gibbs sampler. The applicability is illustrated with two examples. The first analyzes monthly business panel data focusing on the effect of several covariates on a specific ordered response variable. In the second example results of the German soccer league 1993/94 are viewed as response from a dynamic ordered paired comparison system. Here unknown regression parameters corresponding to the underlying time-dependent abilities of the different teams are estimated based on the scores of each game (win-draw-loss)