candidate-set-free algorithm for generating D-optimal split-plot designs

• Published in: Applied statistics Vol. 56; no. 3; pp. 347 - 364
• Main Authors: Jones, Bradley, Goos, Peter
• Format: Journal Article
• Language: English
• Published: Oxford, UK Oxford, UK : Blackwell Publishing Ltd 01.05.2007; Blackwell Publishing Ltd; Blackwell Publishers; Blackwell; Royal Statistical Society; Oxford University Press
• Series: Journal of the Royal Statistical Society Series C
• Subjects: Algorithms; Applications; Candidates; Combinatorics; Combinatorics. Ordered structures; Covariance matrices; D-optimality; Design; Design efficiency; Designs and configurations; Estimation; Exact sciences and technology; Exchange algorithm; Experiment design; Experimental design; Factorial design; Factorials; Hard-to-change factors; Interaction terms; Mathematical models; Mathematics; Mica; Modeling; Multistratum design; Original; Probability and statistics; Regression analysis; Sample size; Sampling; Sampling theory, sample surveys; Sciences and techniques of general use; Specification; Split-plot design; Statistical methods; Statistical models; Statistics; Studies; Tailor-made design; Usefulness; Polynomial; Sample size; Polynomial method; Optimal D design; Linear model; Fixed effect model; Split plot design; Optimal algorithm; Prior distribution; Linear regression; Interaction; Statistical estimation; Fixed effect; Statistics; Statistical regression; Hard-to-change factors; Multistratum design; Regression model; Experimental design; Exchange algorithm; Statistical model; D-optimality; Optimal design(statistics); Tailor-made design; Application; Split-plot design
• ISSN: 0035-9254; 1467-9876; 1467-9876
• DOI: 10.1111/j.1467-9876.2007.00581.x

We introduce a new method for generating optimal split-plot designs. These designs are optimal in the sense that they are efficient for estimating the fixed effects of the statistical model that is appropriate given the split-plot design structure. One advantage of the method is that it does not require the prior specification of a candidate set. This makes the production of split-plot designs computationally feasible in situations where the candidate set is too large to be tractable. The method allows for flexible choice of the sample size and supports inclusion of both continuous and categorical factors. The model can be any linear regression model and may include arbitrary polynomial terms in the continuous factors and interaction terms of any order. We demonstrate the usefulness of this flexibility with a 100-run polypropylene experiment involving 11 factors where we found a design that is substantially more efficient than designs that are produced by using other approaches.