JSM 2005 - Toronto

Abstract #302410

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 204
Type: Invited
Date/Time: Tuesday, August 9, 2005 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract - #302410
Title: Smoothing ANOVA Interactions by Conditioning on Degrees of Freedom
Author(s): Yue Cui and James Hodges*+
Companies: University of Minnesota and University of Minnesota
Address: 2221 University Ave SE, Suite 200, Minneapolis, MN, 55455,
Keywords: Analysis of variance ; Bayesian analysis ; interactions ; prior distributions ; smoothing
Abstract:

Consider a multifactor ANOVA with at least one factor having many levels. Our main example is a prosthodontics dataset in a 2 x 4 x 8 design in which two interactions have 21 degrees of freedom (DF). A 21-DF interaction is an opportunity to discover structure, but also a nuisance: probably only 2 or 3 DF of structure are actually present, and the extra DF may obscure or dilute them. In the classical approach, power can be preserved by prespecifying a few interesting contrasts in the interaction. We present an analysis that avoids the need to prespecify contrasts based on Hodges & Sargent's (Biometrika 2001) definition of DF for hierarchical models. In this paper, the interaction's 21 contrasts are smoothed in a Bayesian manner. The smoothing is controlled by a prior distribution conditioned on the DF in the fit being equal to (say) 3; the data, via the posterior, allocate those DF among the contrasts being smoothed. This analysis has other uses (e.g., analyzing nonreplicated designs without treating all of the highest-order interaction as error). We will specify the model, give an effective MCMC routine, and analyze the main example and others as time permits.

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Revised March 2005