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ForLion: a new algorithm for D-optimal designs under general parametric statistical models with mixed factors

STATISTICS AND COMPUTING 2024年第5期34卷 157-157页

作者： Huang, Yifei Li, Keren Mandal, Abhyuday Yang, Jie Univ Illinois Dept Math Stat & Comp Sci Chicago IL 60607 USA Univ Alabama Birmingham Dept Math Birmingham AL 35294 USA Univ Georgia Dept Stat Athens GA 30602 USA

In this paper, we address the problem of designing an experimental plan with both discrete and continuous factors under fairly general parametric statistical models. We propose a new algorithm, named ForLion, to search for locally optimal approximate designs under the D-criterion. The algorithm performs an exhaustive search in a design space with mixed factors while keeping high efficiency and reducing the number of distinct experimental settings. Its optimality is guaranteed by the general equivalence theorem. We present the relevant theoretical results for multinomial logit models (MLM) and generalized linear models (GLM), and demonstrate the superiority of our algorithm over state-of-the-art design algorithms using real-life experiments under MLM and GLM. Our simulation studies show that the ForLion algorithm could reduce the number of experimental settings by 25% or improve the relative efficiency of the designs by 17.5% on average. Our algorithm can help the experimenters reduce the time cost, the usage of experimental devices, and thus the total cost of their experiments while preserving high efficiencies of the designs.

关键词： ForLion algorithm Generalized linear model lift-one algorithm Mixed factors Multinomial logistic model D-optimal design

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D-OPTIMAL DESIGNS FOR MULTINOMIAL LOGISTIC MODELS

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ANNALS OF STATISTICS 2020年第2期48卷 983-1000页

作者： Bu, Xianwei Majumdar, Dibyen Yang, Jie AbbVie Inc N Chicago IL 60064 USA Univ Illinois Dept Math Stat & Comp Sci Chicago IL USA

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.

关键词： Approximate design exact design Fisher information matrix multinomial response minimally supported design lift-one algorithm

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D-optimal Factorial Designs under Generalized Linear Models

D-optimal Factorial Designs under Generalized Linear Models

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International Conference on Advances in Interdisciplinary Statistics and Combinatorics

作者： Yang, Jie Mandal, Abhyuday Univ Illinois Dept Math Stat & Comp Sci Chicago IL 60680 USA Univ Georgia Dept Stat Athens GA 30602 USA

Generalized linear models (GLMs) have been used widely for modeling the mean response both for discrete and continuous random variables with an emphasis on categorical response. Recently Yang, Mandal and Majumdar (2013) considered full factorial and fractional factorial locally D-optimal designs for binary response and two-level experimental factors. In this article, we extend their results to a general setup with response belonging to a single-parameter exponential family and for multilevel predictors.

关键词： D-optimality Exchange algorithm Factorial design Generalized linear model lift-one algorithm Minimally supported design

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D-optimal Factorial Designs under Generalized Linear Models

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2015年第9期44卷 2264-2277页

作者： Yang, Jie Mandal, Abhyuday Univ Illinois Dept Math Stat & Comp Sci Chicago IL 60680 USA Univ Georgia Dept Stat Athens GA 30602 USA

关键词： D-optimality Exchange algorithm Factorial design Generalized linear model lift-one algorithm Minimally supported design

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