Department of Statistics, Shahid Beheshti University, 1983963113 G.C., Tehran, Iran.
Biostatistics. 2013 Jan;14(1):144-59. doi: 10.1093/biostatistics/kxs028. Epub 2012 Aug 28.
Testing zero variance components is one of the most challenging problems in the context of linear mixed-effects (LME) models. The usual asymptotic chi-square distribution of the likelihood ratio and score statistics under this null hypothesis is incorrect because the null is on the boundary of the parameter space. During the last two decades many tests have been proposed to overcome this difficulty, but these tests cannot be easily applied for testing multiple variance components, especially for testing a subset of them. We instead introduce a simple test statistic based on the variance least square estimator of variance components. With this comes a permutation procedure to approximate its finite sample distribution. The proposed test covers testing multiple variance components and any subset of them in LME models. Interestingly, our method does not depend on the distribution of the random effects and errors except for their mean and variance. We show, via simulations, that the proposed test has good operating characteristics with respect to Type I error and power. We conclude with an application of our process using real data from a study of the association of hyperglycemia and relative hyperinsulinemia.
检验零方差分量是线性混合效应（LME）模型背景下最具挑战性的问题之一。由于零假设位于参数空间的边界上，因此在这种零假设下似然比和得分统计量的常用渐近卡方分布是不正确的。在过去的二十年中，已经提出了许多测试来克服这个困难，但这些测试不能很容易地应用于检验多个方差分量，特别是检验其中的一个子集。相反，我们引入了一个基于方差分量的最小二乘估计的简单检验统计量。随之而来的是一种用于逼近其有限样本分布的置换程序。所提出的检验涵盖了 LME 模型中多个方差分量和任意子集的检验。有趣的是，我们的方法除了依赖于随机效应和误差的均值和方差外，不依赖于它们的分布。我们通过模拟表明，所提出的检验在 I 型错误和功效方面具有良好的运行特性。最后，我们使用高血糖和相对高胰岛素血症关联研究的真实数据应用我们的过程。
