Document Detail

Factor selection and structural identification in the interaction ANOVA model.
MedLine Citation:
PMID:  23323643     Owner:  NLM     Status:  MEDLINE    
When faced with categorical predictors and a continuous response, the objective of an analysis often consists of two tasks: finding which factors are important and determining which levels of the factors differ significantly from one another. Often times, these tasks are done separately using Analysis of Variance (ANOVA) followed by a post hoc hypothesis testing procedure such as Tukey's Honestly Significant Difference test. When interactions between factors are included in the model the collapsing of levels of a factor becomes a more difficult problem. When testing for differences between two levels of a factor, claiming no difference would refer not only to equality of main effects, but also to equality of each interaction involving those levels. This structure between the main effects and interactions in a model is similar to the idea of heredity used in regression models. This article introduces a new method for accomplishing both of the common analysis tasks simultaneously in an interaction model while also adhering to the heredity-type constraint on the model. An appropriate penalization is constructed that encourages levels of factors to collapse and entire factors to be set to zero. It is shown that the procedure has the oracle property implying that asymptotically it performs as well as if the exact structure were known beforehand. We also discuss the application to estimating interactions in the unreplicated case. Simulation studies show the procedure outperforms post hoc hypothesis testing procedures as well as similar methods that do not include a structural constraint. The method is also illustrated using a real data example.
Justin B Post; Howard D Bondell
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Publication Detail:
Type:  Journal Article; Research Support, N.I.H., Extramural; Research Support, U.S. Gov't, Non-P.H.S.     Date:  2013-01-17
Journal Detail:
Title:  Biometrics     Volume:  69     ISSN:  1541-0420     ISO Abbreviation:  Biometrics     Publication Date:  2013 Mar 
Date Detail:
Created Date:  2013-04-08     Completed Date:  2013-10-18     Revised Date:  2014-04-08    
Medline Journal Info:
Nlm Unique ID:  0370625     Medline TA:  Biometrics     Country:  United States    
Other Details:
Languages:  eng     Pagination:  70-9     Citation Subset:  IM    
Copyright Information:
Copyright © 2013, The International Biometric Society.
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MeSH Terms
Age Factors
Analysis of Variance*
Computer Simulation
Models, Statistical*
Grant Support
P01 CA142538/CA/NCI NIH HHS; P01-CA-142538/CA/NCI NIH HHS; R01 MH084022/MH/NIMH NIH HHS; R01-MH-084022/MH/NIMH NIH HHS

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