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:
-
- Arizona State Univ., Phoenix, AZ (United States)
- Arizona State Univ., Tempe, AZ (United States)
- 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
- Alternate Identifier(s):
- OSTI ID: 1691736
- 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. https://doi.org/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. https://doi.org/10.1016/j.chemolab.2019.02.003. https://www.osti.gov/servlets/purl/1511250.
@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 = {Wed Feb 20 00:00:00 EST 2019},
month = {Wed Feb 20 00:00:00 EST 2019}
}
Web of Science