Locally R-optimal designs for a class of nonlinear multiple regression models

Abstract

This paper concerns with optimal designs for a wide class of nonlinear models with information driven by the linear predictor. The aim of this study is to generate an R-optimal design which minimizes the product of the main diagonal entries of the inverse of the Fisher information matrix at certain values of the parameters. An equivalence theorem for the locally R-optimal designs is provided in terms of the intensity function. Analytic solutions for the locally saturated R-optimal designs are derived for the models having linear predictors with and without intercept, respectively. The particle swarm optimization method has been employed to generate locally non-saturated R-optimal designs. Numerical examples are presented for illustration of the locally R-optimal designs for Poisson regression models and proportional hazards regression models.

Keywords:

• Poisson regression models
• proportional hazards models
• R-optimality
• particle swarm optimization

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Lei He's work is supported by the National Natural Science Foundation of China [Grant Number 12101013] and the Natural Science Foundation of Anhui Province [Grant Number 2008085QA15]. Rong-Xian Yue's work is supported by the National Natural Science Foundation of China [Grant Numbers 11971318, 11871143].