A-ComVar: A Flexible Extension of Common Variance Designs

• Published in: Journal of statistical theory and practice Vol. 14; no. 1
• Main Authors: Chowdhury, Shrabanti, Lukemire, Joshua, Mandal, Abhyuday
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.03.2020
• Subjects: Algorithms; Analysis and Advanced Methodologies in the Design of Experiments; Mathematics and Statistics; Original Article; Probability Theory and Stochastic Processes; Statistical Theory and Methods; Statistics; Adaptive lasso; Approximate common variance; Genetic algorithm; Model identification; Common variance; Class of models; Plackett–Burman
• ISSN: 1559-8608; 1559-8616
• DOI: 10.1007/s42519-019-0079-y

We consider nonregular fractions of factorial experiments for a class of linear models. These models have a common general mean and main effects; however, they may have different 2-factor interactions. Here we assume for simplicity that 3-factor and higher-order interactions are negligible. In the absence of a priori knowledge about which interactions are important, it is reasonable to prefer a design that results in equal variance for the estimates of all interaction effects to aid in model discrimination. Such designs are called common variance designs and can be quite challenging to identify without performing an exhaustive search of possible designs. In this work, we introduce an extension of common variance designs called approximate common variance or A-ComVar designs. We develop a numerical approach to finding A-ComVar designs that is much more efficient than an exhaustive search. We present the types of A-ComVar designs that can be found for different number of factors, runs, and interactions. We further demonstrate the competitive performance of both common variance and A-ComVar designs using several comparisons to other popular designs in the literature.