A stochastic unfolding model derived from the partial credit model

Binary preference data can be considered as a special case of incomplete data. Rejection of a item is conceived as an observed response, originating from one of two possible latent responses: rejection because the item is too far to the ’left’ from the respondent’s ideal, or too far to the ’right’. Latent and observed endorsements, however, coincide. The latent responses are modeled through the 3-category Partial Credit Model (PCM). By a reparametrization of the PCM, each item is characterized by a location parameter and a width parameter. Marginal Maximum Likelihood estimators are derived, using the EM-algorithm. A class of statistical tests is derived, which can be used for diagnostic purposes. The ’nuclear energy’ data and the ’traffic’ data are analyzed. A discussion of the ML-estimator of the subject parameter exemplifies the difficulty of the estimation problem.