Constructing D-optimal designs for multi-parameter binary regression models: A theoretical characterization of support points

Abstract

This manuscript presents a comprehensive study on the construction of D-optimal designs for multiparameter binary regression models. The aim is to expand and validate the conjectures put forth by Ford et al. (Ford et al., 1992) regarding D-optimal designs in generalized linear models with multiple parameters. This is based on a parameter dependent transformation to a weighted regression model and results will be extended to other such models. In this study, building upon the pioneering work by Gunduz and Torsney (Gündüz et al., 2023) in univariate settings with two parameters, we extend their methodology to handle the complexities of multiparameter models. By delving into the intricacies of high-dimensional parameter spaces, we address the challenges associated with constructing D-optimal designs for binary regression models, with a specific focus on the rigorous derivation and characterization of the determination of the support points of the design. In summary, our manuscript contributes a significant advancement in the field of experimental design for multiparameter binary regression models. The meticulous mathematical derivations, accompanied by intuitive conceptual plots, provide a comprehensive understanding of our methodology. The compelling simulated examples further emphasize the efficacy of our approach. This work sets the stage for future investigations in adaptive designs, incorporating prior information, and handling complex model structures within the context of D-optimal designs.