Maximum likelihood estimation for Luce's choice model

A terminology for general choice models based on the choice axiom is given. It applies to all kinds of choice experiments, such as confusion choice experiments, paired comparisons, triadic comparisons, directional rankings, scores on binary test items, and others. Maximum likelihood estimation for such general choice models is considered. Conditions for the uniqueness of maximum likelihood estimates are given, and it is shown that the estimates can be derived by iterative proportional fitting. This offers the opportunity of a general test of the choice axiom for all kinds of choice experiments using the likelihood ratio. The estimation and testing procedure is applied to data from a form recognition experiment, reported by W. A. Wagenaar (Nederlands Tijdschrift voor de Psychologie, 1968, 23, 96–108).