Analytic solutions for D-optimal factorial designs under generalized linear models

作者：Tong Liping; Volkmer Hans W; Yang Jie^*

来源：Electronic Journal of Statistics, 2014, 8(1): 1322-1344.

DOI：10.1214/14-EJS926

• Analytic solution
• D-optimal design
• factorial design
• generalized linear model
• Karush-Kuhz-Tucker condition

We develop two analytic approaches to solve D-optimal approximate designs under generalized linear models. The first approach provides analytic D-optimal allocations for generalized linear models with two factors, which include as a special case the 2(2) main-effects model considered by Yang, Mandal and Majumdar [19]. The second approach leads to explicit solutions for a class of generalized linear models with more than two factors. With the aid of the analytic solutions, we provide a necessary and sufficient condition under which a D-optimal design with two quantitative factors could be constructed on the boundary points only. It bridges the gap between D-optimal factorial designs and D-optimal designs with continuous factors.

• 出版日期2014