Computer algorithms of lower-order confounding in regular designs

• Published in: Computational statistics Vol. 39; no. 2; pp. 653 - 676
• Main Authors: Li, Zhi, Li, Zhiming
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2024; Springer Nature B.V
• Subjects: Algorithms; Design of experiments; Economic Theory/Quantitative Economics/Mathematical Methods; Mathematics and Statistics; Original Paper; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Search algorithms; Statistics; General minimum lower-order confounding criterion; Computer algorithm; Aliased component-number pattern; Regular design
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-022-01315-3

In the design of experiments, an optimal design should minimize the confounding between factorial effects, especially main effects and two-factor interaction effects. The general minimum lower-order confounding (GMC) criterion can be used to choose optimal regular designs based on the aliased component-number pattern. This paper aims to study the confounding properties of lower-order effects and provide several computer algorithms to calculate the lower-order confounding in regular designs. We provide a search algorithm to obtain GMC designs. Through python software, we conduct these algorithms. Some examples are analyzed to illustrate the effectiveness of the proposed algorithms.