Abstract

Mixture experiments are used in applications where the proportion of mixing components affects a response variable, such as in studies involving chemical formulations. In many applications, the response is dichotomous or binary (e.g., pass or fail) and a concern for researchers is how to efficiently and informatively design such experiments. A naive approach is to use design recommendations derived from linear normal-theory models with constant variance. In this research, we investigate the potential risks of such designs by comparing them to D-optimal mixture designs for binary responses and evaluating the D-efficiency of these design alternatives for several parameter subspaces. Standard designs for normal theory models generally do not work well for binary responses due to the tendency of these designs to favor boundary points. In addition, D-optimal mixture designs for binary responses tend to locate design points in the region where the magnitude of predicted response probabilities are moderate. We recommend that researchers pay close attention to what is known about the characteristics of the underlying process models in selecting appropriate mixture designs for binary-response applications.

Original languageEnglish (US)
Pages (from-to)11-18
Number of pages8
JournalChemometrics and Intelligent Laboratory Systems
Volume187
DOIs
StatePublished - Apr 15 2019

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Design of experiments
Logistics
Optimal design
Experiments

Keywords

  • Binary responses
  • D-optimality
  • Design assessment
  • Exchange algorithms
  • Experimental design
  • Logistic regression

ASJC Scopus subject areas

  • Analytical Chemistry
  • Software
  • Process Chemistry and Technology
  • Spectroscopy
  • Computer Science Applications

Cite this

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title = "Comparing D-optimal designs with common mixture experimental designs for logistic regression",
abstract = "Mixture experiments are used in applications where the proportion of mixing components affects a response variable, such as in studies involving chemical formulations. In many applications, the response is dichotomous or binary (e.g., pass or fail) and a concern for researchers is how to efficiently and informatively design such experiments. A naive approach is to use design recommendations derived from linear normal-theory models with constant variance. In this research, we investigate the potential risks of such designs by comparing them to D-optimal mixture designs for binary responses and evaluating the D-efficiency of these design alternatives for several parameter subspaces. Standard designs for normal theory models generally do not work well for binary responses due to the tendency of these designs to favor boundary points. In addition, D-optimal mixture designs for binary responses tend to locate design points in the region where the magnitude of predicted response probabilities are moderate. We recommend that researchers pay close attention to what is known about the characteristics of the underlying process models in selecting appropriate mixture designs for binary-response applications.",
keywords = "Binary responses, D-optimality, Design assessment, Exchange algorithms, Experimental design, Logistic regression",
author = "Michelle Mancenido and Rong Pan and Douglas Montgomery and Anderson-Cook, {Christine M.}",
year = "2019",
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AU - Mancenido, Michelle

AU - Pan, Rong

AU - Montgomery, Douglas

AU - Anderson-Cook, Christine M.

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Y1 - 2019/4/15

N2 - Mixture experiments are used in applications where the proportion of mixing components affects a response variable, such as in studies involving chemical formulations. In many applications, the response is dichotomous or binary (e.g., pass or fail) and a concern for researchers is how to efficiently and informatively design such experiments. A naive approach is to use design recommendations derived from linear normal-theory models with constant variance. In this research, we investigate the potential risks of such designs by comparing them to D-optimal mixture designs for binary responses and evaluating the D-efficiency of these design alternatives for several parameter subspaces. Standard designs for normal theory models generally do not work well for binary responses due to the tendency of these designs to favor boundary points. In addition, D-optimal mixture designs for binary responses tend to locate design points in the region where the magnitude of predicted response probabilities are moderate. We recommend that researchers pay close attention to what is known about the characteristics of the underlying process models in selecting appropriate mixture designs for binary-response applications.

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KW - D-optimality

KW - Design assessment

KW - Exchange algorithms

KW - Experimental design

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