Testing the parametric vs the semiparametric generalized mixed effects models

Abstract

The paper presents a study of the generalized partially linear model including random effects in its linear part. For these kinds of models we propose an estimator combining likelihood approaches for mixed effects models with kernel methods. Following the methodology of Härdle et al. (1998), we introduce different tests that allow us to choose between a parametric and the semiparametric mixed effects model. Along these lines we also discuss some bootstrap procedures to simulate the critical values. We prove consistency and give asymptotic theory for all our methods. Finally, a simulation study and a real data application are provided in order to demonstrate the feasibility and the excellent behaviour of our methods