Robustness of Optimal Designs for 2^2 Experiments with Binary Response

TL;DR

This paper investigates the robustness of locally D-optimal designs for 2^2 experiments with binary responses, demonstrating their stability against parameter misspecification through theoretical analysis and simulations.

Contribution

It extends previous work by analyzing the sensitivity of optimal designs to parameter misspecification and applying cylindrical algebraic decomposition for general case design determination.

Findings

Optimal designs are quite robust to parameter misspecification.

Theoretical and simulation results confirm robustness of designs.

Cylindrical algebraic decomposition effectively finds locally D-optimal designs.

Abstract

We consider an experiment with two qualitative factors at 2 levels each and a binary response, that follows a generalized linear model. In Mandal, Yang and Majumdar (2010) we obtained basic results and characterizations of locally D-optimal designs for special cases. As locally optimal designs depend on the assumed parameter values, a critical issue is the sensitivity of the design to misspecification of these values. In this paper we study the sensitivity theoretically and by simulation, and show that the optimal designs are quite robust. We use the method of cylindrical algebraic decomposition to obtain locally D-optimal designs in the general case.