Summary: Sequential Ordinal Modeling with Applications to
James Albert \Lambda
Bowling Green State University, Bowling Green, USA
Washington University, St. Louis, USA
This paper considers the class of sequential probit models in relation to other mod
els for ordinal data. Hierarchical and other extensions of the model are proposed for
applications involving discrete time (grouped) survival data. Computationally practical
Markov chain Monte Carlo algorithms are developed for the fitting of these models. The
ideas and methods are illustrated in detail with a real data example on the length of
hospital stay for patients undergoing heart surgery. A notable aspect of this analysis
is the comparison, based on marginal likelihoods and training sample priors, of several
nonnested models, such as the sequential model, the cumulative ordinal model and
Weibull and loglogistic models.
Keywords: Bayes factor; Discrete hazard function; Gibbs sampling; Marginal likelihood;
MetropolisHastings algorithm; Nonnested models; Sequential probit; Training sample
prior; Model comparison.