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Analysis of Unbalanced Data by Mixed Linear Models Using the mixed Procedure of the SAS System
Authors:J. Spilke  H. P. Piepho   X. Hu
Affiliation:Authors' addresses: Prof. Dr J. Spilke (corresponding author;e-mail: ) and Dr X. Hu, Arbeitsgruppe Biometrie und Agrarinformatik, Martin-Luther-Universität Halle-Wittenberg, 6108 Halle, Ludwig-Wucherer-Straße 82–85, 70593 Stuttgart, Germany;Prof. Dr H. P. Piepho, Institut für Pflanzenbau und Grünland, Universität Hohenheim, Hohenheim, Germany
Abstract:Unbalanced data are a common problem in plant research based on designed experiments. Such data are often conveniently analysed using linear mixed models. Recent developments in mixed model theory have been implemented in major packages. This paper describes the use of the mixed procedure of the SAS System for the analysis of designed experiments. Special emphasis is given to the specification of options as depending on the assumed mixed model and on the unbalancedness in the data. In addition, we consider a compact representation of multiple comparisons for unbalanced data (letter display). Two small data sets are used to exemplify the methods.
Keywords:analysis-of-variance    Kenward    Roger method    restricted maximum likelihood    SAS proc mixed    Satterthwaite method    Wald test
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