Small sample inference for fixed effects from restricted maximum likelihood
Small sample inference for fixed effects from restricted maximum likelihood
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DOI：
10.2307/2533558
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发表时间：
1997-09-01
期刊：
影响因子：
1.9
通讯作者：
Roger, JH
中科院分区：
文献类型：
--
作者：
Kenward, MG;Roger, JH
限制最大似然（REML）是目前公认的一种利用结构协方差矩阵估计一般高斯线性模型参数的方法，特别是用于混合线性模型。传统上，对固定效应的精度估计和推断是基于它们的渐近分布的，这对于一些小样本问题来说是不够的。在本文中，我们提出了一个缩放Wald统计量，以及它的抽样分布的F近似，它在一系列小样本设置中表现良好。统计量使用协方差矩阵的调整估计量，减少了小样本偏差。这种方法的优点是，它在后者是精确的情况下再现统计数据和F分布，即用于Hotelling T-2型统计和方差F比分析。通过对四种不同的REML分析进行仿真研究，评估了改进统计量的性能，并用三个示例说明了这些方法。
Restricted maximum likelihood (REML) is now well established as a method for estimating the parameters of the general Gaussian linear model with a structured covariance matrix, in particular for mixed linear models. Conventionally, estimates of precision and inference for fixed effects are based on their asymptotic distribution, which is known to be inadequate for some small-sample problems. In this paper, we present a scaled Wald statistic, together with an F approximation to its sampling distribution, that is shown to perform well in a range of small sample settings. The statistic uses an adjusted estimator of the covariance matrix that has reduced small sample bias. This approach has the advantage that it reproduces both the statistics and F distributions in those settings where the latter is exact, namely for Hotelling T-2 type statistics and for analysis of variance F-ratios. The performance of the modified statistics is assessed through simulation studies of four different REML analyses and the methods are illustrated using three examples.