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A candidate‐set‐free algorithm for generating D ‐optimal split‐plot designs
Author(s) -
Jones Bradley,
Goos Peter
Publication year - 2007
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/j.1467-9876.2007.00581.x
Subject(s) - categorical variable , set (abstract data type) , plot (graphics) , algorithm , flexibility (engineering) , computer science , mathematical optimization , optimal design , polynomial , mathematics , statistics , machine learning , mathematical analysis , programming language
Summary. 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.