Approximate Model Spaces for Model-Robust Experiment Design

Optimal designs depend upon a prespecified model form. A popular and effective model-robust alternative is to design with respect to a set of models instead of just one. However, model spaces associated with experiments of interest are often prohibitively large and so algorithmically generated designs are infeasible. Here, we present a simple method that largely eliminates this problem by choosing a small set of models that approximates the full set and finding designs that are explicitly robust for this small set. We build our procedure on a restricted columnwise-pairwise algorithm, and explore its effectiveness for two model spaces in the literature. For smaller full model spaces, we find that the designs constructed with the new method compare favorably with robust designs that use the full model space, with construction times reduced by orders of magnitude. We also construct designs that heretofore have been unobtainable due to the size of their model spaces. Supplementary material (available online) includes code, designs, and additional results.

最优试验设计依赖于预先指定的模型形式。一种广为使用且行之有效的模型稳健替代方案，是基于一组模型而非单一模型开展试验设计。然而，与目标实验相关联的模型空间往往大到难以承受，致使算法生成的试验设计方案变得不可行。对此，本文提出一种简单方法：通过选取一组能够近似完整模型空间的小型模型集合，并针对该小型集合构建显式稳健的设计方案，从而在很大程度上解决了上述问题。本方法基于受限逐列成对（restricted columnwise-pairwise）算法构建，并针对文献中的两类模型空间验证了其有效性。对于规模较小的完整模型空间，我们发现采用新方法构建的设计方案，可与使用完整模型空间的稳健设计方案媲美，且构建时间缩减了数个数量级。此外，我们还构建了此前因模型空间规模限制而无法获得的试验设计方案。在线补充材料包含代码、设计方案及额外研究结果。