Maximum Likelihood Unidimensional Unfolding in a Probabilistic Model Without Parametric Assumptions

This paper presents a new probabilistic unidimensional unfolding procedure for paired comparisons data. This procedure is related to a probabilistic unfolding theory in which a nonparametric random ideal coordinate assumption is added to the familiar unidimensional unfolding assumptions. The procedure can be used to find a maximum likelihood sequencing of alternatives or their midpoints, based on choices of a single subject or a group of subjects. It requires a sedation strategy and the calculation of maximum likelihood binomial probability estimates under order restrictions. Algorithms are presented for both purposes. The unfolding procedure can easily be modified to suit related probabilistic unfolding theories.