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

Suppose subjects make repeated responses on the same ordered categoric al scale. We propose a generalization of the Rasch model that expresse s the cumulative legit of the response distribution using subject para meters and a proportional odds structure for item effects. Parameters in the model describe subject-specific, rather than population-average d, 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 parameter s, for the possible binary collapsings of the response. The fitting pr ocess uses an improved Newton-Raphson algorithm for fitting generalize d loglinear models by maximum likelihood estimation subject to constra ints. For the case of two items, we give simple expressions for an eff ect estimate and its standard error, and suggest a test of marginal ho mogeneity for ordinal matched pairs.