Designing Bayesian D-optimal choice experiments with mixtures based on Becker's mixture models

In this paper, Becker's mixture models are first introduced in the literature of choice experiments involving mixtures and Simulated Annealing (SA) and Coordinate-Exchange (CE) algorithms are used to construct the Bayesian D-optimal designs based on these models. Choice experiments are used to understand how product or service attributes shape individual preferences. When attributes are proportions of mixture components, such as in shampoos or snacks, Scheffe's models are often applied, but they are unsuitable for additive component effects. This study uses Becker's mixture models, which support additivity within a multinomial logit framework. Locally D-optimal mixture choice designs use fixed prior vectors, ignoring their uncertainty. To address this, Bayesian D-optimal designs are generated based on multinomial logit model with Becker's mixture models, using simulated annealing (SA) and coordinate-exchange (CE) algorithms. Results indicate that SA performs better than CE in terms of Bayesian D-optimality and increasing prior uncertainty results in higher D-optimality values.