Epsilon Open Archive

Abstract

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.