Mixed model experimental analysis

Dr Chris Brien

PBRC Research Model AnalysisTwo methods of analysis, available for the analysis of designed experiments, are analysis of variance and mixed-model fitting. Brien and Payne (1999) formulate an algorithm for obtaining the analysis of variance for the results of a multitiered experiment. The algorithm has been implemented in the widely available statistical package GenStat (Brien and Payne, 2006). Brien and Demétrio (1998a and b) discuss the multitiered analysis of variance, and its implications, for the particular case of grazing trials.

For mixed model fitting, Brien and Bailey (2006, Section 7) describe a method for deriving a randomization-based mixed model for experiments in general. Brien and Demétrio (2009) extend Brien and Bailey (2006) to explicitly identify terms for which autocorrelation and smooth trend arising from longitudinal observations need to be incorporated in the model. The method is applied to a wide range of examples of longitudinal experiments, including a three-phase, longitudinal experiment to investigate the effect of time of refinement on Eucalyptus pulp from four different sources.


Prof. C. G. B. Demétrio, Departmento de Ciências Exatas, ESALQ, Universidade de São Paulo, Brasil
Prof. R. A. Bailey, School of Mathematical Sciences, Queen Mary, University of London, UK
Prof. R. W. Payne, VSN International, Hemel Hempstead, UK


Brien, C. J. & Bailey, R. A. (2006) Multiple randomizations (with discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology), 68, 571-609.

Brien, C. J. & Demetrio, C. G. B. (1998a) Using the randomisation in specifying the ANOVA model and table for properly and improperly replicated grazing trials. Australian Journal of Experimental Agriculture, 38, 325-334.

Brien, C. J. & Demétrio, C. G. B. (1998b) Using the randomisation in specifying the ANOVA model and table for grazing trials. <http://chris.brien.name/multitier/grazall.ps>.

Brien, C. J. & Demétrio, C. G. B. (2009) Formulating mixed models for experiments, including longitudinal experiments. Journal of Agricultural, Biological and Environmental Sciences, accepted for publication.

Brien, C. J. & Payne, R. W. (1999) Tiers, structure formulae and the analysis of complicated experiments. The Statistician, 48, 41-52.

Brien, C. J. & Payne, R. W. (2006) AMTIER procedure. In Payne, R. W. & Lane, P. W. (Eds.) GenStat Release 9 Reference Manual - Part 3: Procedure Library PL17. Hemel Hempstead, VSN International.

Areas of study and research

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