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

Research output: Contribution to journalArticlepeer-review

Abstract

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

Original languageEnglish (US)
JournalQuality and Reliability Engineering International
DOIs
StateAccepted/In press - 2020

Keywords

  • coordinate exchange
  • D-optimal
  • experimental design
  • logistic regression model
  • nonlinear
  • optimal design
  • separation

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Management Science and Operations Research

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