The Choice Axiom and Independence from Irrelevant Alternatives Property
The Independence from Irrelevant Alternatives (IIA) property is introduced against a background of psychological choice theory, the latter being a composite of L.L. Thurstone's theory of comparative judgement and R.D. Luce's choice axiom, given particular distribution assumptions. Since the IIA condition is both a strength and a potential weakness of the basic and sequential logit models, imposing restrictions on the structure of selection probabilities which may or may not be valid in particular applications, it is necessary to discuss the property in more detail. A simulated data set can be used to illustrate the use of a selected number of tests proposed for identifying whether the IIA property has been violated in a particular application. The IIA assumption has a symmetry property; thus tests of violation that involve changing the number of alternatives in the choice set should include, addition as well as deletion of alternatives.