  Mixed linear models are commonly used in repeated measures studies. They
account for the dependence amongst observations obtained from the same
experimental unit. Oftentimes, the number of observations is small, and it is
thus important to use inference strategies that incorporate small sample
corrections. In this paper, we develop modified versions of the likelihood
ratio test for fixed effects inference in mixed linear models. In particular,
we derive a Bartlett correction to such a test and also to a test obtained from
a modified profile likelihood function. Our results generalize those in Zucker
et al. (Journal of the Royal Statistical Society B, 2000, 62, 827-838) by
allowing the parameter of interest to be vector-valued. Additionally, our
Bartlett corrections allow for random effects nonlinear covariance matrix
structure. We report numerical evidence which shows that the proposed tests
display superior finite sample behavior relative to the standard likelihood
ratio test. An application is also presented and discussed.
