A 2 x 2 Taxonomy of Multilevel Latent Contextual Models: Accuracy-Bias Trade-Offs in Full and Partial Error Correction Models
A 2 x 2 Taxonomy of Multilevel Latent Contextual Models: Accuracy-Bias Trade-Offs in Full and Partial Error Correction Models
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DOI：
10.1037/a0024376
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发表时间：
2011-12-01
影响因子：
7
通讯作者：
Trautwein, Ulrich
中科院分区：
文献类型：
--
作者：
Luedtke, Oliver;Marsh, Herbert W.;Trautwein, Ulrich
在多层建模中，用于评估上下文效应的组级变量（L2）通常是通过聚合来自较低级别（L1）的变量生成的。社会科学语境分析的一个主要问题是，没有无误差的构念测量。在本文中，在估计上下文效应时，多水平数据中出现的两种类型的误差被区分开来：由于测量误差引起的不可靠性和由于抽样误差引起的不可靠性。研究可能会或可能不会纠正这两种类型的误差，这一事实可以转化为2 × 2的多层潜在上下文模型分类，包括4种方法：未纠正方法，部分纠正方法纠正测量或抽样误差（但不是两者），以及完全纠正方法，调整两种误差来源。数学上和模拟数据表明，未校正和部分校正方法可能导致对上下文效应的估计存在很大偏差，这取决于每组L1个体的数量、组的数量、类内相关性、指标的数量和因子负载的大小。然而，模拟研究还表明，当数据仅提供有限的L2结构信息（即组数少，类内相关性低）时，部分校正方法可以优于完全校正方法。本文使用教育心理学的一个实际数据应用来说明不同的方法。
In multilevel modeling, group-level variables (L2) for assessing contextual effects are frequently generated by aggregating variables from a lower level (L1). A major problem of contextual analyses in the social sciences is that there is no error-free measurement of constructs. In the present article, 2 types of error occurring in multilevel data when estimating contextual effects are distinguished: unreliability that is due to measurement error and unreliability that is due to sampling error. The fact that studies may or may not correct for these 2 types of error can be translated into a 2 x 2 taxonomy of multilevel latent contextual models comprising 4 approaches: an uncorrected approach, partial correction approaches correcting for either measurement or sampling error (but not both), and a full correction approach that adjusts for both sources of error. It is shown mathematically and with simulated data that the uncorrected and partial correction approaches can result in substantially biased estimates of contextual effects, depending on the number of L1 individuals per group, the number of groups, the intraclass correlation, the number of indicators, and the size of the factor loadings. However, the simulation study also shows that partial correction approaches can outperform full correction approaches when the data provide only limited information in terms of the L2 construct (i.e., small number of groups, low intraclass correlation). A real-data application from educational psychology is used to illustrate the different approaches.