Optimal Design in Nonlinear Multiresponse Estimation: Poisson Model for Filter Feeding

Larntz, Kinley

doi:10.2307/2532715

Cited by 9 publications

(3 citation statements)

References 32 publications

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“…Some recent works on D‐optimal designs for linear multiresponse models include those of Krafft and Schaefer,34 Bischoff,35 Chang,36, 37 Imhof,38 and Atashgah and Seifi 39. Locally D‐optimal designs for describing the behavior of a biological system were constructed by Hatzis and Larntz40 for nonlinear multiresponse models. Other design criteria for linear multiresponse models include the power criterion of Wijesinha and Khuri41 and the robustness criterion of Wijesinha and Khuri42 and Yue 43…”

Section: Part II Further Developments and The Taguchi Era: 1976–1999mentioning

confidence: 99%

Response surface methodology

Khuri

Mukhopadhyay

2010

WIREs Computational Stats

1,506

588

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The purpose of this article is to provide a survey of the various stages in the development of response surface methodology (RSM). The coverage of these stages is organized in three parts that describe the evolution of RSM since its introduction in the early 1950s. Part I covers the period, 1951–1975, during which the so‐called classical RSM was developed. This includes a review of basic experimental designs for fitting linear response surface models, in addition to a description of methods for the determination of optimum operating conditions. Part II, which covers the period, 1976–1999, discusses more recent modeling techniques in RSM, in addition to a coverage of Taguchi's robust parameter design and its response surface alternative approach. Part III provides a coverage of further extensions and research directions in modern RSM. This includes discussions concerning response surface models with random effects, generalized linear models, and graphical techniques for comparing response surface designs. Copyright © 2010 John Wiley & Sons, Inc. This article is categorized under: Statistical Models > Linear Models Statistical Models > Nonlinear Models

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Section: Part II Further Developments and The Taguchi Era: 1976–1999mentioning

confidence: 99%

Response surface methodology

Khuri

Mukhopadhyay

2010

WIREs Computational Stats

1,506

588

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“…Very little work has been done for multiresponse experiments for GLMs using Bayesian design ideas. Hatzis and Larntz (1992) consider a nonlinear multiresponse model with the probability distribution for the responses given by a Poisson random process. They consider locally D-optimal designs which minimize the generalized variance (volume of the confidence ellipsoid) of the estimated parameters for given specific values of the parameters.…”

Section: Miscellaneous Issues In Bayesian Designmentioning

confidence: 99%

Design Issues for Generalized Linear Models: A Review

Khuri¹,

Mukherjee²,

Sinha³

et al. 2006

Statist. Sci.

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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.Comment: Published at http://dx.doi.org/10.1214/088342306000000105 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

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“…There are many applications of the theory of optimal approximate design in practice and they are increasing. Some recent biomedical applications of these ideas can be found in Hoel and Jennrich," Dunn,13 Hatzis and Larntz,14 Atkinson et al," and Kitsos et a1. 16…”

Section: Summary and Recommendationsmentioning

confidence: 99%

Designing Studies for Dose Response

Wong

Lachenbruch

1996

Statist. Med.

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'Dose response' refers to the regression of a response on a stimulus. We review a number of options for dose-response designs, and compare various designs which may be used in practice. We start with two group designs. Next, we introduce basic optimal approximate design theory for simple linear and quadratic regression illustrating different criteria of optimality and their effect on the allocation of the levels of the dose. Then we obtain the efficiencies of these optimal approximate designs and some simple designs which have intuitive appeal (symmetry, equal spacing of treatments, reduced numbers of observations at the highest and lowest doses).

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Optimal Design in Nonlinear Multiresponse Estimation: Poisson Model for Filter Feeding

Cited by 9 publications

References 32 publications

Response surface methodology

Response surface methodology

Design Issues for Generalized Linear Models: A Review

Designing Studies for Dose Response

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