Computationally Efficient Approaches to Finding Optimal Designs for the Panel Mixed Logit Model
针对面板混合Logit模型信息矩阵计算困难的问题，提出基于惩罚拟似然、边际拟似然和模拟矩法的替代方法，并通过模拟和实例验证其高效性，适用于多属性多选择集的离散选择实验设计。
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 paper, 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.