Statistical Science

Design Issues for Generalized Linear Models: A Review

André I. Khuri, Bhramar Mukherjee, Bikas K. Sinha, and Malay Ghosh

Full-text: Open access

Abstract

Generalized linear models (GLMs) have been used quite effectively in the modeling of a mean response under nonstandard conditions, where discrete as well as continuous data distributions can be accommodated. The choice of design for a GLM is a very important task in the development and building of an adequate model. However, one major problem that handicaps the construction of a GLM design is its dependence on the unknown parameters of the fitted model. Several approaches have been proposed in the past 25 years to solve this problem. These approaches, however, have provided only partial solutions that apply in only some special cases, and the problem, in general, remains largely unresolved. The purpose of this article is to focus attention on the aforementioned dependence problem. We provide a survey of various existing techniques dealing with the dependence problem. This survey includes discussions concerning locally optimal designs, sequential designs, Bayesian designs and the quantile dispersion graph approach for comparing designs for GLMs.

Article information

Source
Statist. Sci., Volume 21, Number 3 (2006), 376-399.

Dates
First available in Project Euclid: 20 December 2006

Permanent link to this document
https://projecteuclid.org/euclid.ss/1166642442

Digital Object Identifier
doi:10.1214/088342306000000105

Mathematical Reviews number (MathSciNet)
MR2339137

Zentralblatt MATH identifier
1246.62168

Keywords
Bayesian design dependence on unknown parameters locally optimal design logistic regression response surface methodology quantal dispersion graphs sequential design

Citation

Khuri, André I.; Mukherjee, Bhramar; Sinha, Bikas K.; Ghosh, Malay. Design Issues for Generalized Linear Models: A Review. Statist. Sci. 21 (2006), no. 3, 376--399. doi:10.1214/088342306000000105. https://projecteuclid.org/euclid.ss/1166642442


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