Multivariate ordinal regression for multiple repeated measurements

In this paper we propose a multivariate ordinal regression model which allows the joint modeling of three-dimensional panel data containing both repeated and multiple measurements for a collection of subjects. This is achieved by a multivariate autoregressive structure on the errors of the latent variables underlying the ordinal responses, where we distinguish between the correlations at a single point in time and the persistence over time. The error distribution is assumed to be normal or Student t distributed. The estimation is performed using composite likelihood methods. We perform several simulation exercises to investigate the quality of the estimates in different settings as well as in comparison with a Bayesian approach. The simulation study confirms that the estimation procedure is able to recover the model parameters well and is competitive in terms of computation time. We also introduce R package mvordflex and illustrate how this implementation can be used to estimate the proposed model in a user-friendly, convenient way. Finally, we illustrate the framework on a data set containing firm failure and credit ratings information from the rating agencies S&P and Moody's for US listed companies.