$D$-Optimal and Nearly $D$-Optimal Exact Designs for Binary Response on the Ball

TL;DR

This paper extends previous results to develop highly efficient, minimally supported D-optimal designs for binary response models with logit and probit links on the ball, simplifying the design process through symmetry considerations.

Contribution

It generalizes existing methods to include symmetric intensity functions, reducing the design system to a single equation and minimizing support points for binary response models.

Findings

Reduced the design system to a single equation using symmetry.

Minimally supported designs are highly efficient.

Results applicable to arbitrary ellipsoidal regions.

Abstract

In this paper the results of Radloff and Schwabe (2019a) will be extended for a special class of symmetrical intensity functions. This includes binary response models with logit and probit link. To evaluate the position and the weights of the two non-degenerated orbits on the $k$-dimensional ball usually a system of three equations has to be solved. The symmetry allows to reduce this system to a single equation. As a further result, the number of support points can be reduced to the minimal number. These minimally supported designs are highly efficient. The results can be generalized to arbitrary ellipsoidal design regions.