## Electronic Journal of Statistics

- Electron. J. Statist.
- Volume 8, Number 1 (2014), 1322-1344.

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

Liping Tong, Hans W. Volkmer, and Jie Yang

#### Abstract

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.

#### Article information

**Source**

Electron. J. Statist., Volume 8, Number 1 (2014), 1322-1344.

**Dates**

First available in Project Euclid: 20 August 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.ejs/1408540289

**Digital Object Identifier**

doi:10.1214/14-EJS926

**Mathematical Reviews number (MathSciNet)**

MR3263124

**Zentralblatt MATH identifier**

1298.62136

**Subjects**

Primary: 62K05: Optimal designs

Secondary: 62K15: Factorial designs

**Keywords**

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

#### Citation

Tong, Liping; Volkmer, Hans W.; Yang, Jie. Analytic solutions for D-optimal factorial designs under generalized linear models. Electron. J. Statist. 8 (2014), no. 1, 1322--1344. doi:10.1214/14-EJS926. https://projecteuclid.org/euclid.ejs/1408540289