Modeling Heterogeneous Variance-Covariance Components in Two-Level Models
Modeling Heterogeneous Variance-Covariance Components in Two-Level Models
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DOI：
10.3102/1076998614546494
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发表时间：
2014-10-01
影响因子：
2.4
通讯作者：
Browne, William
中科院分区：
文献类型：
--
作者：
Leckie, George;French, Robert;Browne, William
多水平模型在连续结果中的应用几乎总是假设残差方差和随机效应方差和协方差为常数。然而，方差的异质性建模可以证明是一个有用的指标，模型的错误指定，在一些教育和行为研究，它甚至可能是直接的实质性利益。这篇文章的目的是回顾，描述和说明一组最近的扩展到两个水平的模型，允许残差和随机效应方差-协方差分量被指定为预测函数。然后，这些预测因子可以输入随机系数，以允许1级异方差关系在2级单位之间变化。我们通过模拟证明，忽略残差方差的2级变异性会导致1级方差函数回归系数的估计具有虚假的精度。我们讨论了软件选项，以适应这些扩展，我们说明他们通过重新分析经典的高中及以后的数据和两个层次的学校的影响模型提出的Raudenbush和Bryk。
Applications of multilevel models to continuous outcomes nearly always assume constant residual variance and constant random effects variances and covariances. However, modeling heterogeneity of variance can prove a useful indicator of model misspecification, and in some educational and behavioral studies, it may even be of direct substantive interest. The purpose of this article is to review, describe, and illustrate a set of recent extensions to two-level models that allow the residual and random effects variance-covariance components to be specified as functions of predictors. These predictors can then be entered with random coefficients to allow the Level-1 heteroscedastic relationships to vary across Level-2 units. We demonstrate by simulation that ignoring Level-2 variability in residual variances leads the Level-1 variance function regression coefficients to be estimated with spurious precision. We discuss software options for fitting these extensions, and we illustrate them by reanalyzing the classic High School and Beyond data and two-level school effects models presented by Raudenbush and Bryk.