Optimal designs for two-level main effects models on a restricted design region

TL;DR

This paper develops $D$-optimal designs for linear main effects models within a restricted subset of the full factorial design, considering bounds on the number of factors at high levels, and finds efficiency varies with margin width.

Contribution

It introduces new $D$-optimal design strategies for models on restricted regions, revealing how margin width influences design structure and efficiency.

Findings

Optimal designs depend on margin width, with narrow margins favoring boundary settings.

Wide margins allow more spread in optimal design points, matching full factorial efficiency.

Results extend to other optimality criteria beyond $D$-optimality.

Abstract

We develop $D$-optimal designs for linear main effects models on a subset of the $2^K$ full factorial design region, when the number of factors set to the higher level is bounded. It turns out that in the case of narrow margins only those settings of the design points are admitted, where the number of high levels is equal to the upper or lower bounds, while in the case of wide margins the settings are more spread and the resulting optimal designs are as efficient as a full factorial design. These findings also apply to other optimality criteria.