d-QPSO: A Quantum-Behaved Particle Swarm Technique for Finding D-Optimal Designs With Discrete and Continuous Factors and a Binary Response

ABSTRACT

Identifying optimal designs for generalized linear models with a binary response can be a challenging task, especially when there are both discrete and continuous independent factors in the model. Theoretical results rarely exist for such models, and for the handful that do, they usually come with restrictive assumptions. In this article, we propose the d-QPSO algorithm, a modified version of quantum-behaved particle swarm optimization, to find a variety of D-optimal approximate and exact designs for experiments with discrete and continuous factors and a binary response. We show that the d-QPSO algorithm can efficiently find locally D-optimal designs even for experiments with a large number of factors and robust pseudo-Bayesian designs when nominal values for the model parameters are not available. Additionally, we investigate robustness properties of the d-QPSO algorithm-generated designs to various model assumptions and provide real applications to design a bio-plastics odor removal experiment, an electronic static experiment, and a 10-factor car refueling experiment. Supplementary materials for the article are available online.

KEYWORDS:

• Approximate design
• Design efficiency
• Equivalence theorem
• Exact design
• Pseudo-Bayesian design

View correction statement:

Correction

Acknowledgments

The authors would like to thank the editor, an associate editor, and the reviewers for comments and suggestions that substantially improved the quality of the article. The second author would like to thank Dr. Snehanshu Saha for his suggestions on the QPSO algorithm.

Funding

The research of Dr. Mandal was in part supported by NSA Grant H98230-13-1-025. The research of Dr. Wong reported in this article was partially supported by the National Institute of General Medical Sciences of the National Institutes of Health under Award Number R01GM107639. The contents in this article are solely the responsibility of the authors and do not necessarily represent the official views of the National Institutes of Health.