Applying Skovgaard's modified directed likelihood statistic to mixed linear models

The introduction of software to calculate maximum likelihood estimates for mixed linear models has made likelihood estimation a practical alternative to methods based on sums of squares. Likelihood based tests and confidence intervals, however, may be misleading in problems with small sample sizes. This paper discusses an adjusted version of the directed log-likelihood statistic for mixed models that is highly accurate for testing one parameter hypotheses. Introduced by Skovgaard (1996, Journal of the Bernoulli Society, 2, 145-165), we show in mixed models that the statistic has a simple compact form that may be obtained from standard software. Simulation studies indicate that this statistic is more accurate than many of the specialized procedures that have been advocated.