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).