Order-of-addition orthogonal arrays to study the effect of treatment ordering
The Annals of Statistics · 2023 · Volume 51 · Issue 4
Abstract
The effect of the order in which a set of m treatments is applied can be modeled by relative-position factors that indicate whether treatment i is carried out before or after treatment j, or by the absolute position for treatment i in the sequence. A design with the same normalized information matrix as the design with all m! sequences is D- and G-optimal for the main-effects model involving the relative-position factors. We prove that such designs are also I-optimal for this model and D-optimal as well as G- and I-optimal for the first-order model in the absolute-position factors. We propose a methodology for a complete or partial enumeration of nonequivalent designs that are optimal for both models.
Keywords
05B20, 62J05, 62K05, Average prediction variance, component-position model, D-optimality, equivalence class, I-optimality, pairwise order factors, projection
Enable JavaScript for citation tools and additional paper interactions.