| We seek to obtain an improved test procedure for fixed effects in general linear models when the sample size is moderate or small. The presence of unknown nuisance parameters or covariance structures often hurt the performance of Wald-type and likelihood ratio (LR) type tests. Using the restricted likelihood in a certain way, we derive a restricted likelihood ratio (RLR) test. The RLR test procedure essentially adjusts the LR test, in a manner that results in improved performance. Furthermore, the RLR test can be easily implemented in more general situations. The characteristics of the RLR test are analytically investigated for a balanced growth curve model with a comparison to the Wald type F test, and simulation studies of tests for several null hypotheses are also considered to demonstrate the consistently good performance of the RLR test. |
