Fast estimation algorithm for likelihood-based analysis of repeated categorical responses

Likelihood-based marginal regression modelling for repeated, or otherwise clustered, categorical responses is computationally demanding. This is because the number of measures needed to describe the associations within a cluster increase geometrically with increasing cluster size. The proposed estimation methods typically describe the associations using odds ratios, which result in computationally unfeasible solutions for large cluster sizes. An alternative method for joint modelling of the regression, association, and dropout mechanism for clustered categorical responses is presented. The joint distribution of a multivariate categorical response is described by utilizing the mean parameterization, which facilitates maximum likelihood estimation in two important respects. The models are illustrated by analyses of the presence and absence of schizophrenia symptoms on 86 patients at 12 repeated time-points, and a survey of opinions of 607 adults regarding government spending on nine different targets, measured on a common 3-level ordinal scale. Free software is available.