Optimal Designs for Two-Stage Inference

TL;DR

This paper introduces a new design criterion for two-stage screening experiments that balances variance, bias, and noise variance estimation, improving upon existing methods especially under model misspecification.

Contribution

It proposes a comprehensive design criterion based on expected confidence intervals and an efficient all-subsets analysis to enhance two-stage experimental designs.

Findings

New designs outperform existing methods in simulations.

The proposed criterion effectively balances all three components of first-stage analysis.

Designs are robust to model misspecification.

Abstract

The analysis of screening experiments is often done in two stages, starting with factor selection via an analysis under a main effects model. The success of this first stage is influenced by three components: (1) main effect estimators' variances and (2) bias, and (3) the estimate of the noise variance. Component (3) has only recently been given attention with design techniques that ensure an unbiased estimate of the noise variance. In this paper, we propose a design criterion based on expected confidence intervals of the first stage analysis that balances all three components. To address model misspecification, we propose a computationally-efficient all-subsets analysis and a corresponding constrained design criterion based on lack-of-fit. Scenarios found in existing design literature are revisited with our criteria and new designs are provided that improve upon existing methods.