We examine the problem of variance components testing in general mixed effects models using the likelihood ratio test. We account for the presence of nuisance parameters, i.e. the fact that some untested variances might also be equal to zero. Two main issues arise in this context leading to a non regular setting. First, under the null hypothesis the true parameter value lies on the boundary of the parameter space. Moreover, due to the presence of nuisance parameters the exact location of these boundary points is not known, which prevents from using classical asymptotic theory of maximum likelihood estimation. Then, in the specific context of nonlinear mixed-effects models, the Fisher information matrix is singular at the true parameter value. We address these two points by proposing a shrinked parametric bootstrap procedure, which is straightforward to apply even for nonlinear models. We show that the procedure is consistent, solving both the boundary and the singularity issues, and we provide a verifiable criterion for the applicability of our theoretical results. We show through a simulation study that, compared to the asymptotic approach, our procedure has a better small sample performance and is more robust to the presence of nuisance parameters. A real data application is also provided.

翻译：本文研究利用似然比检验在一般混合效应模型中进行方差分量检验的问题。我们考虑了扰动参数的存在，即某些未检验的方差也可能为零。该情形下出现两个主要问题导致非正则设定：首先，在原假设下真实参数值位于参数空间边界；其次，由于扰动参数的存在，这些边界点的确切位置未知，这使得经典极大似然估计渐近理论无法直接应用。进一步，在非线性混合效应模型的特定背景下，Fisher信息矩阵在真实参数值处呈现奇异性质。针对这两个问题，我们提出一种收缩型参数Bootstrap方法，该方法即使对于非线性模型也易于实施。我们证明了该方法的相合性，同时解决了边界问题和奇异问题，并给出了理论结果适用性的可验证判据。通过模拟研究表明，与渐近方法相比，我们的方法在小样本下表现更优，且对扰动参数的存在具有更强稳健性。最后提供了真实数据应用案例。