The JML estimation of the generalised unfolding model incorporating the latitude of acceptance parameter

Abstract

Using the hyperbolic cosine model (Andrich & Luo, 1993) as the prototypic model for a single-peaked response process, Luo (in press) introduced a general form for all unidimensional probabilistic unfolding models. In addition to the person and statement location parameters, this general form has an explicit parameter characterising the latitude of acceptance, an important concept in attitude measurement. This general form employs a single operational function, and the difference between various unfolding models is a difference between their operational functions. Because all unfolding models are special cases of the general form, it is possible to develop a general algorithm for the estimation of parameters. With a brief introduction, this paper derives such an algorithm using the joint maximum likelihood principle, which is preferred among various algorithms because it does not require any assumptions about the distribution of person locations. The joint maximum likelihood estimates are not consistent, but a simple correction factor is introduced and shown to work excellently.