Testing variance components in nonlinear mixed effects models.

Abstract : Mixed effects models are widely used to describe heterogeneity in a population, in particular inter and intra individual variabilities. A crucial issue when adjusting such a model to data consists in identifying the fixed and random effects of the model, also called population and individual parameters, respectively. The firstt ones can be considered constant in the population, whereas the second ones vary among individuals. From a statistical point of view, it can be expressed like a test on the nullity of the variances of a given subset of random effects. This issue of variance components testing has been addressed by several authors. In the context of linear mixed effects models, likelihood ratio test procedures have been proposed and results identifying the limiting distribution as well as the finite sample size distribution of the test statistic have been established. Another approach based on the score test is also available. In nonlinear mixed effects models, some authors have also proposed to use the likelihood ratio test. They have established its asymptotic distribution in the particular case of testing thenullity of the variance in a mixed effects model with one single random effect. Indeed, this issue is strongly related to the one of testing parameter values under constraints. In this case, it amounts to testing that the random effect variance parameters are on the boundary of the parameter space. In this paper, we study the likelihood ratio test properties for testing that the variances of a subset of the random effects are equal to zero in a nonlinear mixed effects model, extending the existing results. We prove that the asymptotic distribution of the test statistics is a chi-bar-square distribution, i.e. a mixture of chi-square distributions, and identify the corresponding weights. We highlight in particular that the limiting distribution depends on the presence of correlations between the random effects. We illustrate the finite sample size properties of the test procedure through simulation studies.
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https://hal.archives-ouvertes.fr/hal-01603158
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Submitted on : Monday, October 2, 2017 - 7:36:36 PM
Last modification on : Friday, February 15, 2019 - 11:56:08 AM

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  • HAL Id : hal-01603158, version 1
  • PRODINRA : 391554

Citation

Charlotte Baey, Paul-Henry Cournède, Estelle Kuhn. Testing variance components in nonlinear mixed effects models.. [Technical Report] auto-saisine. 2017, pp.24. ⟨hal-01603158⟩

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