Pure error REML for analyzing data from multi-stratum designs
针对裂区等多层结构设计，提出一种纯误差REML方法估计方差分量，通过将因子水平组合视为离散处理，利用标准软件实现，并采用Kenward-Roger校正改进固定效应标准误估计，在模型误设时更稳健。
Since the dawn of response surface methodology, it has been recommended that designs include replicate points, so that pure error estimates of variance can be obtained and used to provide reliable estimated standard errors of the effects of factors. In designs with more than one stratum, such as split-plot and split-split-plot designs, it is less obvious how pure error estimates of the variance components should be obtained, and no pure error estimates are given by the popular residual maximum likelihood (REML) method of estimation. A method of pure error REML estimation of the variance components, using the full treatment model, is obtained by treating each combination of factor levels as a discrete treatment. This method is easy to implement using standard software and improved estimated standard errors of the fixed effects estimates can be obtained by applying the Kenward-Roger correction based on the pure error REML estimates. The new method is illustrated using several data sets and the performance of pure error REML is compared with the standard REML method. The results are comparable when the assumed response surface model is correct, but the new method is considerably more robust in the case of model misspecification.