Joint work with Charlotte Baey and Paul-Henry Cournède (Ecole Centrale de Paris, MICS)
Mixed effect models are widely used to describe inter and intra individual variabilities in a population. A fundamental question consists in identifying which parameters of the model are shared by all the individuals of the population and which are depending on the considered individual in the population. The first are called fixed effects and the second random effects of the model.
In this talk, we consider this question from a statistical point of view It remains to test if the variances of the considered random effects are equal to zero. The likelihood ratio can be applied, but the assumptions required for standard theoretical results are not fulfilled since the tested parameter values are on the boundary of the parameter space. This question has been addressed in the context of linear mixed effects models by several authors and in the particular case of testing the variance of one single random effect in nonlinear mixed models. We address the case of testing that a subset of the random effect variances are equal to zero considering several random effects possibly correlated. We propose a test procedure based on the likelihood ratio test and establish its theoretical property. In particular, we proof that its asymptotic distribution is a chi bar square distribution. We highlight that the limit distribution depends on the presence of correlation between the random effects. We present numerical tools to compute the corresponding quantiles. Finally, we illustrate the finite sample size properties of the test procedure through simulation studies.