MEANINGFUL REGRESSION AND ASSOCIATION MODELS FOR CLUSTERED ORDINAL DATA

Authors


  • Financial support from the United Kingdom Economic and Social Research Council (award number H333250026), Southampton Statistical Sciences Research Institute, and the Yrjö Jahnsson Foundation is gratefully acknowledged. We thank Anders Ekholm and the anonymous referees for helpful comments.

Abstract

Many proposed methods for analyzing clustered ordinal data focus on the regression model and consider the association structure within a cluster as a nuisance. However, the association structure is often of equal interest—for example, temporal association in longitudinal studies and association between responses to similar questions in a survey. We discuss the use, appropriateness, and interpretability of various latent variable and Markov models for the association structure and propose a new structure that exploits the ordinality of the response. The models are illustrated with a study concerning opinions regarding government spending and an analysis of stability and change in teenage marijuana use over time, where we reveal different behavioral patterns for boys and girls through a comprehensive investigation of individual response profiles.

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