\(A\)-optimal designs under a linearized model for discrete choice experiments (Q2036307)

Discrete choice experiments are applied in order to detect preferences of consumers, customers, patients, etc. Here, a test person is asked to make a choice among certain hypothetical alternatives. The alternatives are arranged in a series of ``choice sets'', each containing a specified number of options/alternatives. In the literature, D-optimal and A-optimal discrete choice designs under the multinomial logit (MNL) model have been developed by a linearization of the MNL. Under certain assumptions of the experimental settings, here, it is shown that the set of A-optimal design that result from this linearization may or may not include the optimal design under the MNL model itself. Then, an alternative linearization is suggested that leads to an information matrix which coincides with that under the MNL-model and, consequently, selects the same set of designs as being A-optimal. Examples of max-contribution A-efficient designs and a practical application are given.