Advances in Small Sample Parametric Inference for Linear Mixed Effects Models

This paper deals with the application of higher order asymptotics for likelihood-based inference to linear mixed effects models. The argument was first introduced by Lyons and Peters (2000) who derived Skovgaard’s second order modification of the signed likelihood ratio statistic for this class of models. They focused on i.i.d within-group errors. We extend their results by considering different heteroscedastic and/or correlated intra-subject variance structures. A number of simulation studies was run which show the improvement that can be achieved by using Skovgaard’s statistic instead of its first order counterpart. The simulations were carried out using a set of routines available in the lme hoa package we implemented in the R programming language. Some details about this software and its applicability will be given.