Multifactor Designs

Jay H. Beder
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Jay H. Beder: University of Wisconsin–Milwaukee

Chapter Chapter 5 in Linear Models and Design, 2022, pp 151-217 from Springer

Abstract: Abstract We study two important decompositions of the parameter space of a factorial model with arbitrarily many factors. The first is the standard breakdown into main effects and interactions, the basis for the analysis of variance. The second, in classical symmetric factorial models, is a finer decomposition into main effects and components of interaction. In both cases we have some algebraic tools to generate effects from other effects. For the former there is a method given by multilinear algebra (the Kirkjian-Zelen construction), while for the latter we have a much more complete theory using the arithmetic of finite fields. A goal is to control confounding with blocks, and both cases rest upon some general results on blocking (partitioning of the set of treatment combinations).

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-08176-7_5

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DOI: 10.1007/978-3-031-08176-7_5

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