On Locally D-optimal Design for Nested Logit Model (Two Nests)

Abstract:Discrete choice experiments play an important role in psychology and market research when measuring the consumerʹs preferences. Usually, the choice behavior is modeled by a multinomial response, where the probabilities of the preferences are given by a logistic model. The resulting "independence of irrelevant alternatives" property of this model, may lead to counter-intuitive results. To avoid these pitfalls, "nested multinomial logit models" have been introduced that allow correlations between the utilities of similar alternatives. In this paper, we consider some choice sets each with the same number of alternatives to obtain locally D-optimal design. In this situation, according to the number of alternatives in each nest there are some classes to define design. Afterward, a design which is produced by combination of designs (related to classes) will be defined and we obtain locally D-optimal deign for it.