Bayesian I-optimal designs for choice experiments with mixtures

TL;DR

This paper develops Bayesian I-optimal designs for choice experiments involving mixtures, emphasizing precise utility predictions, and demonstrates their superiority over D-optimal designs in such contexts.

Contribution

It introduces Bayesian I-optimal design methodology for mixture choice experiments, filling a gap left by previous D-optimal focus, and compares their performance.

Findings

Bayesian I-optimal designs outperform D-optimal designs in predictive accuracy.

I-optimality is more suitable than D-optimality for mixture experiments.

Proposed designs significantly reduce variance in utility predictions.

Abstract

Discrete choice experiments are frequently used to quantify consumer preferences by having respondents choose between different alternatives. Choice experiments involving mixtures of ingredients have been largely overlooked in the literature, even though many products and services can be described as mixtures of ingredients. As a consequence, little research has been done on the optimal design of choice experiments involving mixtures. The only existing research has focused on D-optimal designs, which means that an estimation-based approach was adopted. However, in experiments with mixtures, it is crucial to obtain models that yield precise predictions for any combination of ingredient proportions. This is because the goal of mixture experiments generally is to find the mixture that optimizes the respondents' utility. As a result, the I-optimality criterion is more suitable for designing choice experiments with mixtures than the D-optimality criterion because the I-optimality criterion focuses on getting precise predictions with the estimated statistical model. In this paper, we study Bayesian I-optimal designs, compare them with their Bayesian D-optimal counterparts, and show that the former designs perform substantially better than the latter in terms of the variance of the predicted utility.