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Much Ado About Nothing: the Mixed Models Controversy Revisited

2007; Wiley; Volume: 73; Issue: 1 Linguagem: Inglês

10.1111/j.1751-5823.2005.tb00248.x

1751-5823

Viviana B. Lencina, Júlio M. Singer, Edward J. Stanek,

Statistical Methods and Inference

International Statistical ReviewVolume 73, Issue 1 p. 9-20 Much Ado About Nothing: the Mixed Models Controversy Revisited Viviana B. Lencina, Viviana B. Lencina Departamento de Investigación, FM, Universidad Nacional de Tucumân, ArgentinaSearch for more papers by this authorJulio M. Singer, Julio M. Singer Departamento de Estatstica, IME, Universidade de Sáo Paulo, BrazilSearch for more papers by this authorEdward J. Stanek III, Edward J. Stanek III Department of Biostatistics and Epidemiology, SPH, University of Massachusetts at Amherst, USASearch for more papers by this author Viviana B. Lencina, Viviana B. Lencina Departamento de Investigación, FM, Universidad Nacional de Tucumân, ArgentinaSearch for more papers by this authorJulio M. Singer, Julio M. Singer Departamento de Estatstica, IME, Universidade de Sáo Paulo, BrazilSearch for more papers by this authorEdward J. Stanek III, Edward J. Stanek III Department of Biostatistics and Epidemiology, SPH, University of Massachusetts at Amherst, USASearch for more papers by this author First published: 15 January 2007 https://doi.org/10.1111/j.1751-5823.2005.tb00248.xCitations: 10AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Summaryen We consider a well-known controversy that stems from the use of two mixed models for the analysis of balanced experimental data with a fixed and a random factor. It essentially originates in the different statistics developed from such models for testing that the variance parameter associated to the random factor is null. The corresponding hypotheses are interpreted as that of null random factor main effects in the presence of interaction. The controversy is further complicated by different opinions regarding the appropriateness of such hypothesis. Assuming that this is a sensible option, we show that the standard test statistics obtained under both models are really directed at different hypotheses and conclude that the problem lies in the definition of the main effects and interactions. We use expected values as in the fixed effects case to resolve the controversy showing that under the most commonly used model, the test usually associated to the inexistence of the random factor main effects addresses a different hypothesis. We discuss the choice of models, and some further problems that occur in the presence of unbalanced data. Résuméfr Nous considérons une controverse bien-connue provenant de l'emploi de deux modeles mixtes avec un facteur fixe et un facteur aléatoire pour l'analyse de données expérimentales. Le probléme provient essentiellement des statistiques differentes developpées á partir de ces modéles pour tester que le paramétre de variance associé au facteur aléatoire est nul. Les hypothéses correspondantes sont interprétées comme celles de l'inexistence de l'effet principal du facteur aéatoire en présence de l'intéraction entre les deux facteurs. La controverse est rendue plus complexe encore par les différentes opinions sur la propriété de cette hypothése. En admettant que le choix est sensé, nous montrons que les statistiques usuelles obtenues á partir des deux modéles á s'adressent réellement á des hypothéses différentes et nous arrivons á la conclusion que le probléme est causé par les définitions des effets principaux et de l'interaction. Nous utilisons des valeurs moyennes comme dans le cas de modéles á effets fixés pour résoudre la controverse et nous montrons que selon le modéle plus utilisé, le test généralement associé a l'inexistence de l'effet principal du facteur aléatoire en présence de l'intéraction s'adresse, en realité, á une hypothése différente. Nous discutons du choix des modéles et d'autres problémes qui interviennent en présence de données non-équilibrées. Citing Literature Volume73, Issue1April 2005Pages 9-20 RelatedInformation