A model for overdispersed hierarchical ordinal data

Abstract

Non-Gaussian outcomes are frequently modelled using members of the exponential family. In particular, the Bernoulli model for binary data and the Poisson model for count data are well-known. Two reasons for extending this family are (1) the occurrence of overdispersion, implying that the variability in the data is not adequately described by the models, and (2) the incorporation of hierarchical structure in the data. These issues are routinely addressed separately, the first one through overdispersion models, the second one, for example, by means of random effects within the generalized linear mixed models framework. Molenberghs et al. (2007, 2010) introduced a so-called ‘combined model’ that simultaneously addresses both. In these and subsequent papers, a lot of attention was given to binary outcomes, counts, and time-to-event responses. While common in practice, ordinal data have not been studied from this angle. In this article, a model for ordinal repeated measures, subject to overdispersion, is formulated. It can be fitted without difficulty using standard statistical software. The model is exemplified using data from an epidemiological study in diabetic patients and using data from a clinical trial in psychiatric patients.