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Research article - Peer-reviewed, 2013

Performance of empirical BLUP and Bayesian prediction in small randomized complete block experiments

Forkman, Johannes; Piepho, HP


The model for analysis of randomized complete block (RCB) experiments usually includes two factors: block and treatment. If treatment is modelled as fixed, best linear unbiased estimation (BLUE) is used, and treatment means estimate expected means. If treatment is modelled as random, best linear unbiased prediction (BLUP) shrinks the treatment means towards the overall mean, which results in smaller root-mean-square error (RMSE) in prediction of means. This theoretical result holds provided the variance components are known, but in practice the variance components are estimated. BLUP using estimated variance components is called empirical best linear unbiased prediction (EBLUP). In small experiments, estimates can be unreliable and the usefulness of EBLUP is uncertain. The present paper investigates, through simulation, the performance of EBLUP in small RCB experiments with normally as well as non-normally distributed random effects. The methods of Satterthwaite (1946) and of Kenward & Roger (1997, 2009), as implemented in the SAS System, were studied. Performance was measured by RMSE, in prediction of means, and coverage of prediction intervals. In addition, a Bayesian approach was used for prediction of treatment differences and computation of credible intervals. EBLUP performed better than BLUE with regard to RMSE, also when the number of treatments was small and when the treatment effects were non-normally distributed. The methods of Satterthwaite and of Kenward & Roger usually produced approximately correct coverage of prediction intervals. The Bayesian method gave the smallest RMSE and usually more accurate coverage of intervals than the other methods.


Best linear unbiased prediction; Randomized complete block experiment

Published in

Journal of Agricultural Science
2013, volume: 151, number: 3, pages: 381-395
Publisher: Cambridge University Press

Authors' information

Swedish University of Agricultural Sciences, Department of Crop Production Ecology
Piepho, HP

UKÄ Subject classification

Probability Theory and Statistics

Publication Identifiers


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