Smoothing balanced single-error-term analysis of variance

James S. Hodges; Daniel J. Sargent; Yue Cui; Bradley P. Carlin

doi:10.1198/004017006000000408

Smoothing balanced single-error-term analysis of variance

James S. Hodges, Daniel J. Sargent, Yue Cui, Bradley P. Carlin

Biostatistics

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

We present an approach to smoothing balanced, single-error term analysis of variance (ANOVA), descended from Smith, that also allows spatial, temporal, or spatiotemporal smoothing. The approach addresses unreplicated designs, masked contrasts in effects with many degrees of freedom, and subgroup analysis, demonstrated using a study of denture-lining materials. Our approach is Bayesian but can be viewed as a way to generate frequentist procedures. A simulation experiment compares four priors, unsmoothed ANOVA, and dropping nonsignificant interactions. Three priors have advantages when some interactions are absent; dropping nonsignificant interactions has serious flaws. We contrast our approach with the approaches of Nobile-Green and Gelman.

Original language	English (US)
Pages (from-to)	12-25
Number of pages	14
Journal	Technometrics
Volume	49
Issue number	1
DOIs	https://doi.org/10.1198/004017006000000408
State	Published - Feb 2007

Bibliographical note

Funding Information:
This work was supported in part by National Institute of Allergy and Infectious Diseases (NIAID) contract NO1-AI05073 and NIAID Graduate Training in Biostatistics grant 1-T32- A107432-01A1. The authors thank Tom Louis, the RAND Statistics group, and two referees for helpful comments and Dr. Igor Pesun of the School of Dentistry, University of Minnesota, for permission to use the polishability data.

Keywords

Bayesian analysis
Degrees of freedom
Masking
Prior distribution
Shrinkage
Sub-group analysis

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abstract = "We present an approach to smoothing balanced, single-error term analysis of variance (ANOVA), descended from Smith, that also allows spatial, temporal, or spatiotemporal smoothing. The approach addresses unreplicated designs, masked contrasts in effects with many degrees of freedom, and subgroup analysis, demonstrated using a study of denture-lining materials. Our approach is Bayesian but can be viewed as a way to generate frequentist procedures. A simulation experiment compares four priors, unsmoothed ANOVA, and dropping nonsignificant interactions. Three priors have advantages when some interactions are absent; dropping nonsignificant interactions has serious flaws. We contrast our approach with the approaches of Nobile-Green and Gelman.",

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AU - Sargent, Daniel J.

AU - Cui, Yue

AU - Carlin, Bradley P.

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AB - We present an approach to smoothing balanced, single-error term analysis of variance (ANOVA), descended from Smith, that also allows spatial, temporal, or spatiotemporal smoothing. The approach addresses unreplicated designs, masked contrasts in effects with many degrees of freedom, and subgroup analysis, demonstrated using a study of denture-lining materials. Our approach is Bayesian but can be viewed as a way to generate frequentist procedures. A simulation experiment compares four priors, unsmoothed ANOVA, and dropping nonsignificant interactions. Three priors have advantages when some interactions are absent; dropping nonsignificant interactions has serious flaws. We contrast our approach with the approaches of Nobile-Green and Gelman.

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KW - Degrees of freedom

KW - Masking

KW - Prior distribution

KW - Shrinkage

KW - Sub-group analysis

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Smoothing balanced single-error-term analysis of variance

Abstract

Bibliographical note

Keywords

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