Joint Regression and Association Modeling of Longitudinal Ordinal Data

We propose models for longitudinal, or otherwise clustered, ordinal data. The association between subunit responses is characterized by dependence ratios ( Ekholm, Smith, and McDonald, 1995, Biometrika82, 847–854), which are extended from the binary to the multicategory case. The joint probabilities of the subunit responses are expressed as explicit functions of the marginal means and the dependence ratios of all orders, obtaining a computational advantage for likelihood-based inference. Equal emphasis is put on finding regression models for the univariate cumulative probabilities, and on deriving the dependence ratios from meaningful association-generating mechanisms. A data set on the effects of treatment with Fluvoxamine, which has been analyzed in parts before ( Molenberghs, Kenward, and Lesaffre, 1997, Biometrika84, 33–44), is analyzed in its entirety. Selection models are used for studying the sensitivity of the results to drop-out.