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Title: Variance components testing in mixed effects models with small sample size Authors:  Tom Guedon - Inrae (France) [presenting]
Charlotte Baey - CentraleSupelec (France)
Estelle Kuhn - INRA (France)
Abstract: Mixed-effects models are latent variable models that allow for modeling intra and inter-individual variability in a population. Those models involve two types of effects: the fixed ones common to all individuals and the random effects that vary from one individual to another. Identifying the effects that can be modelled as fixed would reduce the number of parameters, and would also help to identify better the processes that cause the observed variability in the population. Formally, this question can be formulated as a test for the nullity of a block of components of the covariance matrix of the random effects. Since we are interested in an efficient testing procedure with small sample sizes, we propose a parametric bootstrap test procedure. The main issues are the fact that the true values of the variance parameters lie on the boundary of the parameter space, and that the Fisher information matrix is singular under the null hypothesis. Moreover, it is shown here that with a shrunk bootstrap parameter, the bootstrap test is consistent. The performance of the proposed methodology is highlighted through simulation studies.