Fitting unidimensional choice models with nonmetric multidimensional scaling

Abstract

A class of unidimensional choice models is described. Thurstone’s paired comparisons model, Case 5, and the Bradley-Terry-Luce model both fall into the class. A simple nonmetric method is presented for estimating scale values from choice data which satisfy any model in the class. In two examples, nonmetric scale values are compared to Thurstone estimates. The scaling method is extended to permit estimation of scale values in a class of unidimensional ordered-category models, a class which includes the law of categorical judgment.