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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. Lastly, 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.

Authors:
 [1]; ORCiD logo [2];  [2]; ORCiD logo [3]
  1. Arizona State Univ., Phoenix, AZ (United States)
  2. Arizona State Univ., Tempe, AZ (United States)
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE; National Science Foundation (NSF)
OSTI Identifier:
1511250
Report Number(s):
LA-UR-18-31103
Journal ID: ISSN 0169-7439
Grant/Contract Number:  
89233218CNA000001; 1726445
Resource Type:
Accepted Manuscript
Journal Name:
Chemometrics and Intelligent Laboratory Systems
Additional Journal Information:
Journal Volume: 187; Journal Issue: C; Journal ID: ISSN 0169-7439
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
Binary responses; Experimental design; Logistic regression; D-optimality; Design assessment; Exchange algorithms

Citation Formats

Mancenido, Michelle V., Pan, Rong, Montgomery, Douglas C., and Anderson-Cook, Christine M. Comparing D-optimal designs with common mixture experimental designs for logistic regression. United States: N. p., 2019. Web. doi:10.1016/j.chemolab.2019.02.003.
Mancenido, Michelle V., Pan, Rong, Montgomery, Douglas C., & Anderson-Cook, Christine M. Comparing D-optimal designs with common mixture experimental designs for logistic regression. United States. doi:10.1016/j.chemolab.2019.02.003.
Mancenido, Michelle V., Pan, Rong, Montgomery, Douglas C., and Anderson-Cook, Christine M. Wed . "Comparing D-optimal designs with common mixture experimental designs for logistic regression". United States. doi:10.1016/j.chemolab.2019.02.003.
@article{osti_1511250,
title = {Comparing D-optimal designs with common mixture experimental designs for logistic regression},
author = {Mancenido, Michelle V. and Pan, Rong and Montgomery, Douglas C. and Anderson-Cook, Christine M.},
abstractNote = {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. Lastly, 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.},
doi = {10.1016/j.chemolab.2019.02.003},
journal = {Chemometrics and Intelligent Laboratory Systems},
number = C,
volume = 187,
place = {United States},
year = {2019},
month = {2}
}

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This content will become publicly available on February 20, 2020
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