Department of Psychology, University of California, Los Angeles, Los Angeles, California, USA.
University of Notre Dame, Notre Dame, Indiana, USA.
Multivariate Behav Res. 2020 Jan-Feb;55(1):120-136. doi: 10.1080/00273171.2019.1627513. Epub 2019 Jun 27.
Inference of variance components in linear mixed modeling (LMM) provides evidence of heterogeneity between individuals or clusters. When only nonnegative variances are allowed, there is a boundary (i.e., 0) in the variances' parameter space, and regular inference statistical procedures for such a parameter could be problematic. The goal of this article is to introduce a practically feasible permutation method to make inferences about variance components while considering the boundary issue in LMM. The permutation tests with different settings (i.e., constrained vs. unconstrained estimation, specific vs. generalized test, different ways of calculating values, and different ways of permutation) were examined with both normal data and non-normal data. In addition, the permutation tests were compared to likelihood ratio (LR) tests with a mixture of chi-squared distributions as the reference distribution. We found that the unconstrained permutation test with the one-sided -value approach performed better than the other permutation tests and is a useful alternative when the LR tests are not applicable. An R function is provided to facilitate the implementation of the permutation tests, and a real data example is used to illustrate the application. We hope our results will help researchers choose appropriate tests when testing variance components in LMM.
在线性混合模型 (LMM) 中推断方差分量提供了个体或聚类之间存在异质性的证据。当只允许非负方差时，方差参数空间中存在一个边界（即 0），并且针对此类参数的常规推断统计程序可能会出现问题。本文的目的是引入一种实用可行的置换方法，以便在考虑 LMM 中的边界问题的同时，对方差分量进行推断。使用正态数据和非正态数据检验了具有不同设置的置换检验（即受约束与不受约束的估计、特定与广义检验、不同的 值计算方法以及不同的置换方法）。此外，还将置换检验与具有混合卡方分布的似然比 (LR) 检验进行了比较，作为参考分布。我们发现，具有单边 - 值方法的无约束置换检验比其他置换检验表现更好，并且当 LR 检验不适用时，是一种有用的替代方法。提供了一个 R 函数来方便实施置换检验，并使用真实数据示例来说明应用。我们希望我们的结果将帮助研究人员在测试 LMM 中的方差分量时选择适当的检验。
