Designs for Generalized Linear Models With Several Variables and Model Uncertainty

Woods, David C.; Lewis, S. M.; Eccleston, J. A.; Russell, K. G.

doi:10.1198/004017005000000571

Cited by 133 publications

(126 citation statements)

References 36 publications

Supporting

Mentioning

125

Contrasting

Unclassified

Order By: Relevance

“…Following terminology given by Woods, Lewis, Eccleston and Russell (2006), a compromise D-optimal design over m alternative models is one which maximizes the following criterion:…”

Section: Compromise Designmentioning

confidence: 99%

“…Examples follow including the design of a seven-factor screening experiment from Wu and Hamada (2000) which demonstrates how to apply our methods in practice. Other examples are considered to compare computational approaches from the literature (Woods, Lewis, Eccleston and Russell (2006) and Gotwalt, Jones and Steinberg (2009)) with our simpler and more efficient techniques.…”

Section: Introductionmentioning

confidence: 99%

“…However, recently there have been substantial advances in developing algorithmic approaches to generate robust designs which provide a means of addressing this complication. These advances have come from Woods, Lewis, Eccleston and Russell (2006), Dror and Steinberg (2006) and Gotwalt, Jones and Steinberg (2009). In order to apply these methods, uncertainty is described in the form of a probability distribution (or prior), and the objective is to then find a design that performs well over this uncertainty.…”

Section: Introductionmentioning

confidence: 99%

“…We consider these conditions, and show how our methods can be easily extended for implementation in practice. Woods, Lewis, Eccleston and Russell (2006) introduced the idea of a compromise design, which is a robust design found by optimizing across many parameter sets simultaneously through the implementation of a compound criterion. In what follows, we define an 'average' model and show how it can be used to find an analytical solution for robust designs.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Robust Designs for Poisson Regression Models

McGree¹,

Eccleston²

2012

Technometrics

View full text Add to dashboard Cite

We consider the problem of how to construct robust designs for Poisson regression models. An analytical expression is derived for robust designs for first-order Poisson regression models where uncertainty exists in the prior parameter estimates. Given cer-tain constraints in the methodology, it may be necessary to extend the robust designs for implementation in practical experiments. With these extensions, our methodology constructs designs which perform similarly, in terms of estimation, to current techniques, and offers the solution in a more timely manner. We further apply this analytic result to cases where uncertainty exists in the linear predictor. The application of this method-ology to practical design problems such as screening experiments is explored. Given the minimal prior knowledge that is usually available when conducting such experiments, it is recommended to derive designs robust across a variety of systems. However, in-corporating such uncertainty into the design process can be a computationally intense exercise. Hence, our analytic approach is explored as an alternative. AbstractWe consider the problem of how to construct robust designs for Poisson regression models. An analytical expression is derived for robust designs for first-order Poisson regression models where uncertainty exists in the prior parameter estimates. Given certain constraints in the methodology, it may be necessary to extend the robust designs for implementation in practical experiments. With these extensions, our methodology constructs designs which perform similarly, in terms of estimation, to current techniques, and offers the solution in a more timely manner. We further apply this analytic result to cases where uncertainty exists in the linear predictor. The application of this methodology to practical design problems such as screening experiments is explored. Given the 1 Author to whom correspondence should be addressed.2 minimal prior knowledge that is usually available when conducting such experiments, it is recommended to derive designs robust across a variety of systems. However, incorporating such uncertainty into the design process can be a computationally intense exercise. Hence, our analytic approach is explored as an alternative.

show abstract

“…Following terminology given by Woods, Lewis, Eccleston and Russell (2006), a compromise D-optimal design over m alternative models is one which maximizes the following criterion:…”

Section: Compromise Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust Designs for Poisson Regression Models

McGree¹,

Eccleston²

2012

Technometrics

View full text Add to dashboard Cite

show abstract

“…Sinha and Wiens (2002) consider the construction of sequential designs which are robust against model uncertainty for nonlinear models. Further results on misspecified nonlinear regression include Woods et al (2006), Wiens and Xu (2008) and Xu (2009a) for prediction and extrapolation problems.…”

Section: Introductionmentioning

confidence: 99%

Model robust designs for survival trials

Konstantinou

Biedermann

Kimber

2017

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

The exponential-based proportional hazards model is often assumed in timeto-event experiments but may only approximately hold. We consider deviations in different neighbourhoods of this model that include other widely used parametric proportional hazards models and we further assume that the data are subject to censoring. Minimax designs are then found explicitly based on criteria corresponding to classical c-and D-optimality. We provide analytical characterisations of optimal designs which, unlike optimal designs for related problems in the literature, have finite support and thus avoid the issues of implementing a density-based design in practice. Finally, our designs are compared with the balanced design that is traditionally used in practice, and recommendations for practitioners are given.

show abstract

Central Composite Designs

Draper

2007

Encyclopedia of Statistics in Quality and Reliability

View full text Add to dashboard Cite

Choosing a suitable experimental design is an important first step in investigations of the factors that may influence one or more response variables. Such investigations often lead to the representation of the response variable as a second‐order (quadratic) surface in the predictor variables. Central composite‐type designs are popular, classical, and excellent choices for this purpose. A portion of a design of this type can be performed initially to fit a first‐order model. A second‐order portion can then be added, if it becomes clear that the first‐order fit suggests the need for supplementary information. A three‐predictor variable data set is worked through to illustrate the decisions involved in these types of studies.

show abstract

Designs for Generalized Linear Models With Several Variables and Model Uncertainty

Cited by 133 publications

References 36 publications

Robust Designs for Poisson Regression Models

Robust Designs for Poisson Regression Models

Model robust designs for survival trials

Central Composite Designs

Contact Info

Product

Resources

About