A compound optimality criterion for D‐efficient and separation‐robust designs for the logistic regression model

Abstract

AbstractThe ‐criterion is proposed to generate optimal designs for the logistic regression model with reduced separation probabilities. This compound criterion has two components: (a) the ‐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 ‐optimal design maximizes the ‐criterion. The aim is to obtain compromise experimental designs with high ‐efficiencies that are more robust to separation than a ‐optimal design of equal size. This paper presents the ‐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 ‐optimal designs offer a 20‐30% reduction in separation probability over the local ‐optimal designs while maintaining ‐efficiencies over 93%. A robust design methodology is also demonstrated, where a robust ‐optimal design is compared to a Bayesian ‐optimal design and shown to have comparable ‐efficiencies across a range of randomly drawn parameter values while offering a mean reduction in separation probability of 23.9%.