Improved small sample inference in the mixed linear model: Bartlett correction and adjusted likelihood

The mixed linear model is a popular method for analysing unbalanced repeate d measurement data. The classical statistical tests for parameters in this model are based on asymptotic theory that is unreliable in the small sample s that are often encountered in practice. For testing a given fixed effect parameter with a small sample, we develop and investigate refined likelihoo d ratio (LR) tests. The refinements considered are the Bartlett correction and use of the Cox-Reid adjusted likelihood; these are examined separately and in combination. We illustrate the various LR tests on an actual data se t and compare them in two simulation studies. The conventional LR test yiel ds type I error rates that are higher than nominal. The adjusted LR test yi elds rates that are lower than nominal, with absolute accuracy similar to t hat of the conventional LR test in the first simulation study and better in the second. The Bartlett correction substantially improves the accuracy of the type I error rates with either the conventional or the adjusted LR tes t. In many cases, error rates that are very close to nominal are achieved w ith the refined methods.