Department of Methodology of the Behavioral Sciences, Faculty of Psychology, University of Barcelona, Passeig de la Vall d'Hebron, 171, 08035, Barcelona, Spain.
Behav Res Methods. 2012 Dec;44(4):1224-38. doi: 10.3758/s13428-012-0196-y.
Using a Monte Carlo simulation and the Kenward-Roger (KR) correction for degrees of freedom, in this article we analyzed the application of the linear mixed model (LMM) to a mixed repeated measures design. The LMM was first used to select the covariance structure with three types of data distribution: normal, exponential, and log-normal. This showed that, with homogeneous between-groups covariance and when the distribution was normal, the covariance structure with the best fit was the unstructured population matrix. However, with heterogeneous between-groups covariance and when the pairing between covariance matrices and group sizes was null, the best fit was shown by the between-subjects heterogeneous unstructured population matrix, which was the case for all of the distributions analyzed. By contrast, with positive or negative pairings, the within-subjects and between-subjects heterogeneous first-order autoregressive structure produced the best fit. In the second stage of the study, the robustness of the LMM was tested. This showed that the KR method provided adequate control of Type I error rates for the time effect with normally distributed data. However, as skewness increased-as occurs, for example, in the log-normal distribution-the robustness of KR was null, especially when the assumption of sphericity was violated. As regards the influence of kurtosis, the analysis showed that the degree of robustness increased in line with the amount of kurtosis.
本文运用蒙特卡罗模拟和肯沃德-罗杰（KR）自由度校正方法，分析了线性混合模型（LMM）在混合重复测量设计中的应用。LMM 首先用于选择具有三种数据分布（正态、指数和对数正态）的协方差结构。结果表明，当组间协方差具有同质性且分布为正态时，最佳拟合的协方差结构是无结构总体矩阵。然而，当组间协方差具有异质性且协方差矩阵与组大小的配对为零时，最佳拟合是具有异质性的无结构总体矩阵，所有分析的分布都是如此。相比之下，当配对为正或负时，个体内和个体间异质一阶自回归结构产生最佳拟合。在研究的第二阶段，检验了 LMM 的稳健性。结果表明，KR 方法在数据正态分布时，为时间效应提供了充分的 I 型错误率控制。然而，随着偏度的增加（例如，在对数正态分布中），KR 的稳健性为零，尤其是当违反球形假设时。关于峰度的影响，分析表明，随着峰度的增加，稳健性的程度也随之增加。
