This article surveys various strategies for modeling ordered categorical (ordinal) response variables when the data have some type of clustering, extending a similar survey for binary data by Pendergast, Gange, Newton, Lindstrom, Palta & Fisher (1996). An important special case is when repeated measurement occurs at various occasions for each subject, such as in longitudinal studies. A much greater variety of models and fitting methods are available than when a similar survey for repeated ordinal response data was prepared a decade ago (Agresti, 1989). The primary emphasis of the review is on two cla.s.ses of models, marginal models for which effects are averaged over all clusters at particular levels of predictors, and cluster-specific models for which effects apply at the cluster level. We present the two types of models in the ordinal context, review the literature for each, and discuss connections between them. Then, we summarize some alternative modeling approaches and ways of estimating parameters, including a Bayesian approach. We also discuss applications and areas likely to be popular for future research, such as ways of handling missing data and ways of modeling agreement and evaluating the accuracy of diagnostic tests. Finally, we review the current availability of software for using the methods discussed in this article. 18 2 4 11 14 22 Source: Fmcom, Chunag-Skin & Landis (1989)
Cluster-specific and Marginal ModelsIn the formulation of models, we refer to the sampling units as clusters. In many applications, such as Table 1, each cluster is a set of repeated measurements on a subject. In others, each cluster is a set of subjects expected to be more similar to each other than to other subjects, such as a litter of mice in a teratology study.As with binary and other forms of categorical data (Pendergast et al., 1996), two major types of model for ordinal responses differ in terms of whether they have population-averaged or clusterspecijc (sometimes called subject-specific) effects. The latter models refer to conditional distributions at the cluster (e.g., subject) level, whereas the former models refer to marginal distributions, averaged over clusters in the population. The choice of model affects whether parameter interpretations apply at the cluster or the population level (Zeger, Liang & Albert, 1988; Neuhaus, Kalbfleisch & Hauck, 1991;Ten Have, Landis & Hartzel, 1996). Population-level interpretations are more relevant in epidemiological studies that focus on overall frequency of occurrence in a population. As we will discuss in Section 3.2, approximate relationships exist between population-averaged parameters in marginal models and corresponding parameters in cluster-specific models; however, a cluster-specific model usually does not imply a marginal model of the same form, and a marginal model need not have any simple and meaningful cluster-specific model that implies it. A third type of model, called a transition model, is used in longitudinal studies to describe the distribution of a respons...