### 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 language | English (US) |
---|---|

Pages (from-to) | 11-18 |

Number of pages | 8 |

Journal | Chemometrics and Intelligent Laboratory Systems |

Volume | 187 |

DOIs | |

State | Published - Apr 15 2019 |

### Fingerprint

### 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

**Comparing D-optimal designs with common mixture experimental designs for logistic regression.** / Mancenido, Michelle; Pan, Rong; Montgomery, Douglas; Anderson-Cook, Christine M.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Comparing D-optimal designs with common mixture experimental designs for logistic regression

AU - Mancenido, Michelle

AU - Pan, Rong

AU - Montgomery, Douglas

AU - Anderson-Cook, Christine M.

PY - 2019/4/15

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.

AB - 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.

KW - Binary responses

KW - D-optimality

KW - Design assessment

KW - Exchange algorithms

KW - Experimental design

KW - Logistic regression

UR - http://www.scopus.com/inward/record.url?scp=85061928657&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061928657&partnerID=8YFLogxK

U2 - 10.1016/j.chemolab.2019.02.003

DO - 10.1016/j.chemolab.2019.02.003

M3 - Article

VL - 187

SP - 11

EP - 18

JO - Chemometrics and Intelligent Laboratory Systems

JF - Chemometrics and Intelligent Laboratory Systems

SN - 0169-7439

ER -