A General Formulation for Unidimensional Unfolding and Pairwise Preference Models: Making Explicit the Latitude of Acceptance.

Probabilistic unfolding models for direct responses of persons to statements are characterised by single peaked response functions. The range in which a positive response is most likely is termed the latitude of acceptance, a well known but little researched concept in the modelling of attitude measurement. This paper derives a general form for probabilistic unfolding models in which a natural parameter characterises the latitude of acceptance. It is shown that a number of already known models for unfolding can be reexpressed in this general form with different operational functions and that, in doing so, the implied latitude of acceptance for these models is identified. It is also shown that other unfolding models can be generated readily by specifying the operational function of the general form. A general form for pairwise preference models is also presented. A discussion on the latitude of acceptance parameter as a scale parameter is also provided. Copyright 1998 Academic Press.