Marginal Modeling of Correlated Ordinal Data Using a Multivariate Plackett Distribution

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Abstract
An extension of the bivariate model suggested by Dale is proposed for the analysis of dependent ordinal categorical data. The so-called multivariate Dale model is constructed by first generalizing the bivariate Plackett distribution to any dimensions. Because the approach is likelihood based, it satisfies properties that are not fulfilled by other popular methods, such as the generalized estimating equations approach. The proposed method models both the marginal and the association structure in a flexible way. The attractiveness of the multivariate Dale model is illustrated in three key examples, covering areas such as crossover trials, longitudinal studies with patients dropping out from the study, and discriminant analysis applications. The differences and similarities with the generalized estimating approach are highlighted.

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