Optimality of multi-way designs

TL;DR

This paper investigates the optimality of dual multi-way designs derived from orthogonal plans, demonstrating their M-optimality and extending previous results in the field of experimental design.

Contribution

It introduces the concept of duals of orthogonal plans in multi-way settings and proves their M-optimality, generalizing earlier findings.

Findings

Duals of certain orthogonal plans are M-optimal.

Constructed new multi-way designs that are proven to be M-optimal.

Extended previous results to broader classes of multi-way designs.

Abstract

In this paper we study optimality aspects of a certain type of designs in a multi-way heterogeneity setting. These are ``duals" of plans orthogonal through the block factor (POTB). Here by the dual of a main effect plan (say $\rho$) we mean a design in a multi-way heterogeneity setting obtained from $\rho$ by interchanging the roles of the block factors and the treatment factors. Specifically, we take up two series of universally optimal POTBs for symmetrical experiments constructed in Morgan and Uddin (1996). We show that the duals of these plans, as multi-way designs, satisfy M-optimality. Next, we construct another series of multiway designs and proved their M-optimality, thereby generalising the result of Bagchi and Shah (1989). It may be noted that M-optimality includes all commonly used optimality criteria like A-, D- and E-optimality.