Locally $D$-optimal Designs for a Wider Class of Non-linear Models on the $k$-dimensional Ball with applications to logit and probit models

TL;DR

This paper extends the theory of locally D-optimal experimental designs to a broader class of non-linear models, including logit and probit, on k-dimensional balls, using invariance principles and allowing approximate designs.

Contribution

It generalizes previous results to more non-linear models and arbitrary ellipsoidal regions, introducing approximate designs for the first time in this context.

Findings

Derived locally D-optimal designs for binary response models.

Extended design region from spheres to ellipsoids.

Introduced the use of invariance and equivariance in design construction.

Abstract

In this paper we extend the results of Radloff and Schwabe (2018), which could be applied for example to Poisson regression, negative binomial regression and proportional hazard models with censoring, to a wider class of non-linear multiple regression models. This includes the binary response models with logit and probit link besides other. For this class of models we derive (locally) $D$-optimal designs when the design region is a $k$-dimensional ball. For the corresponding construction we make use of the concept of invariance and equivariance in the context of optimal designs as in our previous paper. In contrast to the former results the designs will not necessarily be exact designs in all cases. Instead approximate designs can appear. These results can be generalized to arbitrary ellipsoidal design regions.