Linear Mixed Effects Models under Inequality Constraints with Applications
Linear Mixed Effects Models under Inequality Constraints with Applications
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DOI：
10.1371/journal.pone.0084778
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发表时间：
2014-01-21
期刊：
影响因子：
3.7
通讯作者：
Peddada, Shyamal D.
中科院分区：
文献类型：
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作者：
Farnan, Laura;Ivanova, Anastasia;Peddada, Shyamal D.
在流行病学、生物学、毒理学等许多科学实验/研究中自然会出现限制，研究人员在分析数据并使用方差分析 (ANOVA) 等标准方法时常常忽略这些信息。这种方法不仅可能导致实验成本方面的动力和效率损失，而且还可能导致数据解释不佳。在本文中，我们讨论在许多应用中自然出现的线性混合效应模型背景下的约束统计推断，例如重复测量设计、家族研究等。我们引入了一种新颖的方法，该方法广泛适用于参数的各种约束。由于在许多应用中样本量很小和/或数据不一定是正态分布的，而且误差方差不必是同方差的（即数据中的异质性），我们使用经验最佳线性无偏预测器（EBLUP）类型基于残差的引导方法来导出所提出的测试的临界值。我们的模拟研究表明，所提出的程序保持了所需的标称 I 类误差，同时在功率方面与其他测试竞争良好。我们通过重新分析血汞水平的临床试验数据来说明所提出的方法。本文介绍的方法可以轻松扩展到其他设置，例如非线性和广义回归模型。
Constraints arise naturally in many scientific experiments/studies such as in, epidemiology, biology, toxicology, etc. and often researchers ignore such information when analyzing their data and use standard methods such as the analysis of variance (ANOVA). Such methods may not only result in a loss of power and efficiency in costs of experimentation but also may result poor interpretation of the data. In this paper we discuss constrained statistical inference in the context of linear mixed effects models that arise naturally in many applications, such as in repeated measurements designs, familial studies and others. We introduce a novel methodology that is broadly applicable for a variety of constraints on the parameters. Since in many applications sample sizes are small and/or the data are not necessarily normally distributed and furthermore error variances need not be homoscedastic (i.e. heterogeneity in the data) we use an empirical best linear unbiased predictor (EBLUP) type residual based bootstrap methodology for deriving critical values of the proposed test. Our simulation studies suggest that the proposed procedure maintains the desired nominal Type I error while competing well with other tests in terms of power. We illustrate the proposed methodology by re-analyzing a clinical trial data on blood mercury level. The methodology introduced in this paper can be easily extended to other settings such as nonlinear and generalized regression models.