D-OPTIMAL DESIGNS FOR MULTINOMIAL LOGISTIC MODELS

• 成果类型: Article
• 署名作者: Bu, Xianwei; Majumdar, Dibyen; Yang, Jie
• 署名单位: AbbVie; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1834
• 发表日期: 2020
• 页码: 983-1000
• 关键词: regression-models

摘要

We consider optimal designs for general multinomial logistic models, which cover baseline-category, cumulative, adjacent-categories and continuation-ratio logit models, with proportional odds, nonproportional odds or partial proportional odds assumption. We derive the corresponding Fisher information matrices in three different forms to facilitate their calculations, determine the conditions for their positive definiteness, and search for optimal designs. We conclude that, unlike the designs for binary responses, a feasible design for a multinomial logistic model may contain less experimental settings than parameters, which is of practical significance. We also conclude that even for a minimally supported design, a uniform allocation, which is typically used in practice, is not optimal in general for a multinomial logistic model. We develop efficient algorithms for searching D-optimal designs. Using examples based on real experiments, we show that the efficiency of an experiment can be significantly improved if our designs are adopted.