广义线性模型下D-最优析因设计的解析解
Analytic Solutions for D-optimal Factorial Designs under Generalized Linear Models
摘要：
我们发展了两种解析方法来求解广义线性模型下的D-最优近似设计。第一种方法为具有两个因子的广义线性模型提供了解析D-最优分配，其中包括Yang，Mandal and Majumdar（2012）考虑的$2^2$主效应模型作为特例。第二种方法给出了一类含两个以上因子的广义线性模型的显式解。借助于解析解，我们给出了一个仅在边界点上可构造两个定量因子的D-最优设计的充分必要条件。它弥补了D-最优析因设计和具有连续因子的D-最优设计之间的差距。
英文摘要：
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 (2012). 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.
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