Copt Samuel, Heritier Stephane
NHMRC Clinical Trials Centre, University of Sydney, Australia.
Biometrics. 2007 Dec;63(4):1045-52. doi: 10.1111/j.1541-0420.2007.00804.x. Epub 2007 May 2.
Mixed linear models are commonly used to analyze data in many settings. These models are generally fitted by means of (restricted) maximum likelihood techniques relying heavily on normality. The sensitivity of the resulting estimators and related tests to this underlying assumption has been identified as a weakness that can even lead to wrong interpretations. Very recently a highly robust estimator based on a scale estimate, that is, an S-estimator, has been proposed for general mixed linear models. It has the advantage of being easy to compute and allows the computation of a robust score test. However, this proposal cannot be used to define a likelihood ratio type test that is certainly the most direct route to robustify an F-test. As the latter is usually a key tool of hypothesis testing in mixed linear models, we propose two new robust estimators that allow the desired extension. They also lead to resistant Wald-type tests useful for testing contrasts and covariate effects. We study their properties theoretically and by means of simulations. The analysis of a real data set illustrates the advantage of the new approach in the presence of outlying observations.
混合线性模型在许多情况下常用于分析数据。这些模型通常通过（受限）极大似然技术进行拟合，该技术严重依赖于正态性。已确定所得估计量及相关检验对这一基本假设的敏感性是一个弱点，甚至可能导致错误的解释。最近，针对一般混合线性模型，有人提出了一种基于尺度估计的高度稳健估计量，即S估计量。它具有易于计算的优点，并允许计算稳健得分检验。然而，该提议不能用于定义似然比类型检验，而这肯定是使F检验稳健化的最直接途径。由于后者通常是混合线性模型中假设检验的关键工具，我们提出了两种新的稳健估计量，它们允许进行所需的扩展。它们还会产生用于检验对比和协变量效应的稳健Wald型检验。我们从理论上和通过模拟研究了它们的性质。对一个实际数据集的分析说明了新方法在存在异常观测值情况下的优势。
