Lazar Ann A, Zerbe Gary O
University of California, San Francisco.
J Educ Behav Stat. 2011 Dec;36(6):699-719. doi: 10.3102/1076998610396889.
Researchers often compare the relationship between an outcome and covariate for two or more groups by evaluating whether the fitted regression curves differ significantly. When they do, researchers need to determine the "significance region," or the values of the covariate where the curves significantly differ. In analysis of covariance (ANCOVA), the Johnson-Neyman procedure can be used to determine the significance region; for the hierarchical linear model (HLM), the Miyazaki and Maier (M-M) procedure has been suggested. However, neither procedure can assume nonnormally distributed data. Furthermore, the M-M procedure produces biased (downward) results because it uses the Wald test, does not control the inflated Type I error rate due to multiple testing, and requires implementing multiple software packages to determine the significance region. In this article, we address these limitations by proposing solutions for determining the significance region suitable for generalized linear (mixed) model (GLM or GLMM). These proposed solutions incorporate test statistics that resolve the biased results, control the Type I error rate using Scheffé's method, and uses a single statistical software package to determine the significance region.
研究人员通常通过评估拟合回归曲线是否存在显著差异，来比较两个或多个组的结果与协变量之间的关系。当存在显著差异时，研究人员需要确定“显著区域”，即曲线存在显著差异时协变量的值。在协方差分析（ANCOVA）中，可使用约翰逊 - 奈曼程序来确定显著区域；对于分层线性模型（HLM），有人建议使用宫崎和迈尔（M - M）程序。然而，这两种程序都不能假定数据为非正态分布。此外，M - M程序会产生有偏差（向下）的结果，因为它使用了 Wald 检验，没有控制由于多次检验导致的第一类错误率膨胀，并且需要使用多个软件包来确定显著区域。在本文中，我们通过提出适用于广义线性（混合）模型（GLM 或 GLMM）的显著区域确定解决方案，来解决这些局限性。这些提出的解决方案纳入了检验统计量，可解决有偏差的结果，使用谢费方法控制第一类错误率，并使用单个统计软件包来确定显著区域。
