Second-Order Likelihood-Based Inference in Mixed-Effects Models.

This paper focuses on the application of higher-order asymptotics for likelihood-based inference to mixed-effects models. In particular, for a scalar parameter of interest, the modified directed likelihood of Skovgaard (1996) is considered. Its expression in linear and nonlinear mixed-effects models with a single level of grouping is derived, starting from the results of Lyons and Peters (2000). Some simulation studies demonstrate the improvements that can be obtained by using this statistic with respect to first-order methods.