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：本文研究了在一般混合效应模型中使用似然比检验进行方差分量检验的问题。我们考虑了冗余参数的存在，即某些未检验的方差可能同样为零的情况。在此背景下，两个主要问题导致了一个非正则设定：首先，在原假设下真实参数值位于参数空间的边界；其次，由于冗余参数的存在，这些边界点的确切位置未知，这使得经典的最大似然估计渐近理论无法适用。特别在非线性混合效应模型中，Fisher信息矩阵在真实参数值处呈现奇异性。针对这两个问题，我们提出了一种收缩参数Bootstrap方法，该方法即使对于非线性模型也易于实施。我们证明了该程序具有一致性，能同时解决边界问题和奇异性问题，并提供了理论结果适用性的可验证准则。通过模拟研究，我们发现相较于渐近方法，本程序在小样本情况下表现更优，且对冗余参数的存在具有更强的稳健性。文中还提供了实际数据应用案例。