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 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.
Funding Statement
The research of the first author was funded by Fonds Wetenschappelijk Onderzoek—FWO Flanders.
Acknowledgments
This research was started during a visit of the authors to the School of Statistics and Data Science, Nankai University, Tianjin, PR China. We are grateful to Professor M.Q. Liu for his warm hospitality during this visit. We are also grateful to José Nuñez Áres for his help with accessing the multithread workstation. The comments of a referee helped us to shorten the proof of our Theorems 1 and 2.
Citation
Eric D. Schoen. Robert W. Mee. "Order-of-addition orthogonal arrays to study the effect of treatment ordering." Ann. Statist. 51 (4) 1877 - 1894, August 2023. https://doi.org/10.1214/23-AOS2317
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