Hyperbolic Cosine Latent Trait Models for Unfolding Direct Responses and Pairwise Preferences
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In this paper, the hyperbolic cosine unfolding model for direct responses of persons to individual stimuli is elabo rated in three ways: the parameter of the stimu lus, which reflects a region within which people located there are more likely to respond positively than negatively, is shown to be a property of the data and not arbitrary as first supposed.Abstract:
The hyperbolic cosine unfolding model for direct responses of persons to individual stimuli is elabo rated in three ways. First, the parameter of the stimu lus, which reflects a region within which people located there are more likely to respond positively than negatively, is shown to be a property of the data and not arbitrary as first supposed. Second, the model is used to construct a related model for pairwise preferences. This model, for which joint maximum likelihood estimates are derived, satisfies strong sto chastic transitivity. Third, the role of substantive theory in evaluating the fit between the data and the models, in which unique solutions for the estimates are not guaranteed, is explored by analyzing responses of one group of persons to a single set of stimuli obtained both as direct responses and pairwise preferences.read more
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TL;DR: In this paper, a rating response mechanism for ordered categories, which is related to the traditional threshold formulation but distinctively different from it, is formulated, in which subject and item parameters are derived in terms of thresholds on a latent continuum and discriminations at the thresholds.