Abstract

Decomposing variables into between and within components are often required in multilevel analysis. This method of decomposition should not ignore possible unreliability of an observed group mean (i.e., arithmetic mean) that is due to small cluster sizes and can lead to substantially biased estimates. Adjustment procedures that allow unbiased estimation have been defined and implemented in software for a two-level model. This study shows how to implement a two-stage adjustment procedure in a three-level design. A simulation study showed that the adjustment procedure provides unbiased estimates. To demonstrate how the adjustment procedure can change results in a real data context, an illustration is provided using a set up in which 355 Level-1 units are nested in 93 Level-2 and 19 Level-3 units.

摘要

在多级分析中通常需要将变量分解为组件之间和组件内。这种分解方法不应忽略观察到的组平均值（即算术平均值）的可能不可靠性，这是由于集群大小较小并且可能导致估计有很大偏差。允许无偏估计的调整程序已在软件中定义和实施，用于两级模型。本研究展示了如何在三水平设计中实施两阶段调整程序。一项模拟研究表明，调整程序提供了无偏估计。为了演示调整过程如何在真实数据环境中改变结果，我们使用一个设置进行了说明，其中 355 个 Level-1 单元嵌套在 93 个 Level-2 和 19 个 Level-3 单元中。