Design Issues for Generalized Linear Models: A Review

By A. I. Khuri, Bhramar Mukherjee, Bikas K. Sinha, Malay Ghosh. 2006

148 citations recorded by the source corpus.

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.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/79ae29f47531295b121135dc8994d2657248025b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Management Science and Operations Research

1. Min Yang
2. John Stufken
3. Holger Dette
4. Viatcheslav B. Melas
5. Bin Zhang
6. Shuguang Huang

In Statistics and Probability

1. Min Yang
2. John Stufken
3. Holger Dette
4. Viatcheslav B. Melas
5. I. Van Keilegom
6. Natalie Neumeyer
7. Johan Segers
8. Stanislav Volgushev

Citations in the corpus

• IDENTIFYING LOCALLY OPTIMAL DESIGNS FOR NONLINEAR MODELS: A SIMPLE EXTENSION WITH PROFOUND CONSEQUENCES (2012, methodology): “The argument that our method can immediately be applied for the multistage approach is exactly as in Yang and Stufken (2009). For a broader discussion on the challenges to identify optimal designs for generalized linear models, many of which apply also for other nonlinear models, we refer the reader”
• A note on the de la Garza phenomenon for locally optimal designs (2011, background): “in the sub-class of all saturated designs. In a celebrated paper, de la Garza (1954) proved that for a (p−1)th-degree polynomial regression model, any optimal design can be based on at most p points. Khuri et al. (2006) considered a nonlinear regression model and introduced the terminology of the de”
• OPTIMAL DESIGNS FOR GENERALIZED LINEAR MODELS WITH MULTIPLE DESIGN VARIABLES (2011, background): “Khuri et al. (2006) surveyed design issues for GLMs and pointed out that results on designs for generalized linear models with multiple covariates requires extensive work to evaluate “optimal” or, at least, efficient designs.”