ENBIS-17 in Naples

9 – 14 September 2017; Naples (Italy) Abstract submission: 21 November 2016 – 10 May 2017

George Box Award: Jeff Wu. Award Talk on "A Fresh Look at Effect Aliasing and Interactions: Some New Wine in Old Bottles"

11 September 2017, 14:50 – 15:50


Submitted by
Jeff Wu
Jeff Wu (Georgia Tech)
Interactions and effect aliasing are among the most fundamental concepts in experimental design. In this paper, some new insights and approaches are provided on these time-honored subjects. Start with the two-level fractional factorial designs. In the literature, the “de-aliasing” or estimation of aliased effects is deemed to be impossible. We argue that this “impossibility” can indeed be resolved by employing a new approach which reparametrizes effects using the notion of “conditional main effects” (cme’s), then performs model selection by exploiting the properties between the cme’s and traditional factorial effects. In some sense, this is a shocking result, because the impossibility has been taken for granted since the founding work of Finney (1945). This approach can be extended beyond designed experiments to general observational data using bi-level variable selection techniques. There is a similar surprise for three-level fractional factorial designs. The standard approach is to use ANOVA to decompose the interactions into orthogonal components. Then the quandary of full aliasing between interaction components remains. Again, this can be resolved by using a non-orthogonal decomposition with the linear-quadratic parametrization. Then a model search strategy would allow the estimation of some interaction components even for designs of resolution III and IV. Moving from regular to nonregular designs, most of the interactions are not orthogonal to the main effects. The partial aliasing of effects can be exploited for the estimation of interactions. The common theme underlying the three problems is the use of reparametrization and exploitation of non-orthogonality among effects. A historical recollection is given on how these ideas were conceived and discovered over a period of nearly 30 years.

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