On the Efficiency of Generally Balanced Designs Analysed by Restricted Maximum Likelihood
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Restricted maximum likelihood (reml) is commonly used in the analysis of incomplete block designs. With this method, treatment contrasts are estimated by generalized least squares, using an estimated variance-covariance matrix of the observations as if it were known. This leads to under-estimation of the variance of treatment contrasts, because uncertainty on the variance components is not adequately taken into account. To correct for this bias, Kackar and Harville (1984) and Kenward and Roger (1997) propose adjusted estimators of the treatment variance-covariance matrix, based on Taylor series expansions.
We consider small experiments with an orthogonal block structure. The adjusted estimator of Kenward and Roger (1997) is calculated when the design is generally balanced. A small modification is proposed that leads to a simple expression for the adjustment, as a function of the efficiency factors of the design, the variance components and the dimensions of the block strata. The behaviour of the adjusted estimator is assessed through a simulation study based on a semi-Latin square for twelve treatments.
Keywordsgenerally balanced design restricted maximum likelihood
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