Optimal row-column designs

• 成果类型: Article
• 署名作者: Zhou, Zheng; Zhou, Yongdao
• 署名单位: Nankai University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asac046
• 发表日期: 2023
• 关键词: microarray experiments; factorial-designs; CONSTRUCTION; plans

摘要

Row-column designs have been widely used in experiments involving double confounding. Among them, one that provides unconfounded estimation of all main effects and as many two-factor interactions as possible is preferred, and is called optimal. Most current work focuses on the construction of two-level row-column designs, while the corresponding optimality theory has been largely ignored. Moreover, most constructed designs contain at least one replicate of a full factorial design, which is not flexible as the number of factors increases. In this study, a theoretical framework is built up to evaluate the optimality of row-column designs with prime level. A method for constructing optimal row-column designs with prime level is proposed. Subsequently, optimal full factorial three-level row-column designs are constructed for any parameter combination. Optimal fractional factorial two-level and three-level row-column designs are also constructed for cost saving.