Open Access
April 2020 D-optimal designs for multinomial logistic models
Xianwei Bu, Dibyen Majumdar, Jie Yang
Ann. Statist. 48(2): 983-1000 (April 2020). DOI: 10.1214/19-AOS1834


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.


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Xianwei Bu. Dibyen Majumdar. Jie Yang. "D-optimal designs for multinomial logistic models." Ann. Statist. 48 (2) 983 - 1000, April 2020.


Received: 1 August 2018; Revised: 1 February 2019; Published: April 2020
First available in Project Euclid: 26 May 2020

zbMATH: 07241577
MathSciNet: MR4102684
Digital Object Identifier: 10.1214/19-AOS1834

Primary: 62K05
Secondary: 62J12

Keywords: approximate design , exact design , Fisher information matrix , lift-one algorithm , minimally supported design , multinomial response

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 2 • April 2020
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