A compound optimality criterion for D‐efficient and separation‐robust designs for the logistic regression model. (23rd September 2020)

• Record Type: Journal Article
• Authors: Park, Anson R.; Mancenido, Michelle V.; Montgomery, Douglas C.
• Editors: Medlin, Rebecca M.
• Is Part Of: Quality and reliability engineering international. Volume 37:Number 7(2021)
• Page Start: 3066
• Page End: 3083
• Publication Date: 2020-09-23
• Subjects: coordinate exchange -- D‐optimal -- experimental design -- logistic regression model -- nonlinear -- optimal design -- separation; Reliability (Engineering) -- Periodicals; Quality control -- Periodicals; High technology -- Periodicals; 620.00452
• DOI: 10.1002/qre.2768
• Languages: English
• ISSNs: 0748-8017

Abstract

Abstract: The D M P ‐criterion is proposed to generate optimal designs for the logistic regression model with reduced separation probabilities. This compound criterion has two components: (a) the D ‐efficiency of the candidate design and (b) a penalty term that captures the average distance of the candidate design's support points from the region of maximum prediction variance (MPV). A D M P ‐optimal design maximizes the D M P ‐criterion. The aim is to obtain compromise experimental designs with high D ‐efficiencies that are more robust to separation than a D ‐optimal design of equal size. This paper presents the D M P ‐criterion and demonstrates examples of its potential use as a means of mitigating separation in the design phase of a binary response experiment. For the examples presented, the local D M P ‐optimal designs offer a 20‐30% reduction in separation probability over the local D ‐optimal designs while maintaining D ‐efficiencies over 93%. A robust design methodology is also demonstrated, where a robust D M P ‐optimal design is compared to a Bayesian D ‐optimal design and shown to have comparable D ‐efficiencies across a range of randomly drawn parameter values while offering a mean reduction in separation probability of 23.9%.