Efficient Designs With Minimal Aliasing

• Published in: Technometrics Vol. 53; no. 1; pp. 62 - 71
• Main Authors: Jones, Bradley, Nachtsheim, Christopher J.
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.02.2011; The American Society for Quality and The American Statistical Association; American Society for Quality and the American Statistical Association; American Society for Quality
• Subjects: Absolute value; Alias matrix; Bayesian design; Constrained design; D-optimality; Design efficiency; Design optimization; Estimating techniques; Estimation bias; Exact sciences and technology; Experiment design; Experimental design; Factorial design; Mathematics; Matrix; Minimum bias design; Modeling; Probability and statistics; Response surface design; Sciences and techniques of general use; Statistical bias; Statistical models; Statistical variance; Statistics; Bayes estimation; Response surface design; Bias; Bayesian design; Medical screening; Modeling; Optimal design; Constrained optimization; Screening; Alias matrix; Minimum bias design; Experimental design; Constrained design; Response surface; D-optimality; Optimal design(statistics)
• ISSN: 0040-1706; 1537-2723
• DOI: 10.1198/TECH.2010.09113

For some experimenters, a disadvantage of the standard optimal design approach is that it does not consider explicitly the aliasing of specified model terms with terms that are potentially important but are not included in the model. For example, when constructing an optimal design for a first-order model, aliasing of main effects and interactions is not considered. This can lead to designs that are optimal for estimation of the primary effects of interest, yet have undesirable aliasing structures. In this article, we construct exact designs that minimize the squared norm of the alias matrix subject to constraints on design efficiency. We demonstrate use of the method for the construction of screening and response surface designs.