Computationally Efficient Approaches to Finding Optimal Designs for the Panel Mixed Logit Model

Discrete choice experiments (DCEs) are popular in business, marketing, health sciences, and many other fields. Panel mixed logit models are a special case of generalized linear mixed models that are natural choices for analyzing data arising from such experiments. In this article, we propose techniques for identifying optimal designs for panel mixed logit models. Here the information matrix does not have a closed form expression and is computationally intensive to evaluate numerically, which to date has made finding designs under these models using search algorithms difficult. To overcome this difficulty, we propose using alternative forms of the information matrix based on penalized quasi-likelihood (PQL), marginal quasi-likelihood (MQL) and the method of simulated moments (MSM). Our simulation results suggest that PQL is the best option when a design with a very high efficiency is required, but that the significantly faster MQL may be acceptable in many cases. We use the proposed methods to search for D-optimal designs for two nontrivial DCE examples reported in literature with a large number of attributes and choice sets, which would be prohibitively expensive using existing techniques. All approaches are implemented in an R package.