A PROPORTIONAL ODDS MODEL WITH SUBJECT-SPECIFIC EFFECTS FOR REPEATED ORDERED CATEGORICAL RESPONSES

Suppose subjects make repeated responses on the same ordered categorical scale. We propose a generalization of the Rasch model that expresses the cumulative logit of the response distribution using subject parameters and a proportional odds structure for item effects. Parameters in the model describe subject-specific, rather than population-averaged, effects. Consistent estimation of the-effects requires eliminating the subject parameters. We accomplish this by simultaneous fitting of Rasch models, conditional on sufficient statistics for those parameters, for the possible binary collapsings of the response. The fitting process uses an improved Newton-Raphson algorithm for fitting generalized loglinear models by maximum likelihood estimation subject to constraints. For the case of two items, we give simple expressions for an effect estimate and its standard error, and suggest a test of marginal homogeneity for ordinal matched pairs.