Optimum Designs for a Multiresponse Regression Model

Imhof, Lorens A.

doi:10.1006/jmva.1999.1841

Cited by 18 publications

(3 citation statements)

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“…Wijesinha and Khuri33 later modified Fedorov's procedure by using an estimate of \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{amsfonts}\pagestyle{empty}\begin{document}$\sum$\end{document} at each step of the sequential process. 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.…”

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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“…Krafft and Schaefer [19] and Chang [4] studied some properties of multiresponse. Imhof [12] and Chang et al [5] also studied some examples of multiresponse. Liu and Yue [23] developed some multiresponse theorems.…”

Section: Introductionmentioning

confidence: 99%

Equivalence theorem of $D$-optimal equal allocation design for multiresponse mixture experiments

Zhu

Hao

et al. 2021

Hacettepe Journal of Mathematics and Statistics

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The equivalence theorem is the most important theorem of experimental design. For single response, the D-optimal equivalence theorem of the continuous design and equal allocation design already exist. However, the equivalence theorem of D-optimal equal allocation design for multiresponse mixture experiments has not been investigated. In this paper, we study this problem and find that the maximize of the variance function of the equivalence theorem equal to the number of response. D-optimal designs for multiresponse are illustrated by two examples.

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“…For example, Chang (1997) developed an algorithm to generate near D-optimal designs, and the models include mainly the first-order or second-order polynomial model for each response. Imhof (2000) found exact optimal designs for a bivariate model where each mean response is modeled by a linear and a quadratic model and the joint responses may be correlated. Wang (2000) discussed exact and approximate D-optimal designs for multi-response polynomial models.…”

Section: Introductionmentioning

confidence: 99%

Optimal Designs for Multi-Response Nonlinear Regression Models With Several Factors via Semidefinite Programming

Wong

Yin

Zhou

2018

Journal of Computational and Graphical Statistics

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We use semi-definite programming (SDP) to find a variety of optimal designs for multiresponse linear models with multiple factors, and for the first time, extend the methodology to find optimal designs for multi-response nonlinear models and generalized linear models with multiple factors. We construct transformations that (i) facilitate improved formulation of the optimal design problems into SDP problems, (ii) enable us to extend SDP methodology to find optimal designs from linear models to nonlinear multi-response models with multiple factors and (iii) correct erroneously reported optimal designs in the literature caused by formulation issues. We also derive invariance properties of optimal designs and their dependence on the covariance matrix of the correlated errors, which are helpful for reducing the computation time for finding optimal designs. Our applications include finding A-, As-, c- and D-optimal designs for multi-response multi-factor polynomial models, locally c- and D-optimal designs for a bivariate Emax response model and for a bivariate Probit model useful in the biosciences.

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Optimum Designs for a Multiresponse Regression Model

Cited by 18 publications

References 10 publications

Response surface methodology

Response surface methodology

Equivalence theorem of $D$-optimal equal allocation design for multiresponse mixture experiments

Optimal Designs for Multi-Response Nonlinear Regression Models With Several Factors via Semidefinite Programming

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