Penalized likelihood ratio tests for repeated measurement models

In this paper, we propose a novel test procedure for repeated measurements based on the penalized likelihood ratio (PLR). The procedure provides an alternative to the standard likelihood ratio tests for evaluating null hypotheses concerning the correlation structure of repeated measurements. PLR tests are specifically designed for nonstandard test situations where non-identifiability of a nuisance parameter occurs under the null hypothesis. The idea is to penalize the estimation close to the boundary of the domain of the nuisance parameter and thereby eliminate the non-identifiability. We show that the asymptotic distribution of the PLR test is a 50:50 mixture of chi-square distributions with 0 and 1 degrees of freedom. Simulation studies indicate that the asymptotic distribution of the PLR test provides a good approximation, even for fairly small data sets (10-20 subjects). A sensitivity analysis with a real data example highlights the strengths and weaknesses of the test procedure.