Verbeke Geert, Molenberghs Geert
Biostatistical Centre, Catholic University of Leuven, U.Z. St.-Rafaël, Kapucijnenvoer 35, B-3000 Leuven, Belgium.
Biometrics. 2003 Jun;59(2):254-62. doi: 10.1111/1541-0420.00032.
Whenever inference for variance components is required, the choice between one-sided and two-sided tests is crucial. This choice is usually driven by whether or not negative variance components are permitted. For two-sided tests, classical inferential procedures can be followed, based on likelihood ratios, score statistics, or Wald statistics. For one-sided tests, however, one-sided test statistics need to be developed, and their null distribution derived. While this has received considerable attention in the context of the likelihood ratio test, there appears to be much confusion about the related problem for the score test. The aim of this paper is to illustrate that classical (two-sided) score test statistics, frequently advocated in practice, cannot be used in this context, but that well-chosen one-sided counterparts could be used instead. The relation with likelihood ratio tests will be established, and all results are illustrated in an analysis of continuous longitudinal data using linear mixed models.
每当需要对方差分量进行推断时，单侧检验和双侧检验之间的选择至关重要。这种选择通常取决于是否允许出现负方差分量。对于双侧检验，可以基于似然比、得分统计量或Wald统计量遵循经典的推断程序。然而，对于单侧检验，需要开发单侧检验统计量，并推导其零分布。虽然这在似然比检验的背景下受到了相当多的关注，但对于得分检验的相关问题似乎存在很多混淆。本文的目的是说明，实践中经常提倡的经典（双侧）得分检验统计量在此情况下不能使用，但可以使用精心选择的单侧对应统计量取而代之。将建立与似然比检验的关系，并通过使用线性混合模型对连续纵向数据进行分析来说明所有结果。
