Marsh Herbert W, Lüdtke Oliver, Robitzsch Alexander, Trautwein Ulrich, Asparouhov Tihomir, Muthén Bengt, Nagengast Benjamin
a University of Oxford , UK.
b Max Planck Institute for Human Development , Berlin , Germany.
Multivariate Behav Res. 2009 Nov 30;44(6):764-802. doi: 10.1080/00273170903333665.
This article is a methodological-substantive synergy. Methodologically, we demonstrate latent-variable contextual models that integrate structural equation models (with multiple indicators) and multilevel models. These models simultaneously control for and unconfound measurement error due to sampling of items at the individual (L1) and group (L2) levels and sampling error due the sampling of persons in the aggregation of L1 characteristics to form L2 constructs. We consider a set of models that are latent or manifest in relation to sampling items (measurement error) and sampling of persons (sampling error) and discuss when different models might be most useful. We demonstrate the flexibility of these 4 core models by extending them to include random slopes, latent (single-level or cross-level) interactions, and latent quadratic effects. Substantively we use these models to test the big-fish-little-pond effect (BFLPE), showing that individual student levels of academic self-concept (L1-ASC) are positively associated with individual level achievement (L1-ACH) and negatively associated with school-average achievement (L2-ACH)-a finding with important policy implications for the way schools are structured. Extending tests of the BFLPE in new directions, we show that the nonlinear effects of the L1-ACH (a latent quadratic effect) and the interaction between gender and L1-ACH (an L1 × L1 latent interaction) are not significant. Although random-slope models show no significant school-to-school variation in relations between L1-ACH and L1-ASC, the negative effects of L2-ACH (the BFLPE) do vary somewhat with individual L1-ACH. We conclude with implications for diverse applications of the set of latent contextual models, including recommendations about their implementation, effect size estimates (and confidence intervals) appropriate to multilevel models, and directions for further research in contextual effect analysis.
本文是方法与实质内容的协同。在方法上，我们展示了整合结构方程模型（具有多个指标）和多层模型的潜在变量情境模型。这些模型同时控制并消除因个体（L1）和组（L2）层面的项目抽样导致的测量误差，以及因将L1特征汇总形成L2结构时人员抽样导致的抽样误差。我们考虑了一组与项目抽样（测量误差）和人员抽样（抽样误差）相关的潜在或显性模型，并讨论了不同模型在何时可能最有用。我们通过扩展这些核心模型以纳入随机斜率、潜在（单水平或跨水平）交互作用和潜在二次效应，展示了它们的灵活性。在实质上，我们使用这些模型来检验大鱼小池塘效应（BFLPE），结果表明学生个体层面的学业自我概念（L1 - ASC）与个体层面的成绩（L1 - ACH）呈正相关，与学校平均成绩（L2 - ACH）呈负相关——这一发现对学校结构设置方式具有重要的政策意义。在将BFLPE的测试拓展到新方向时，我们发现L1 - ACH的非线性效应（潜在二次效应）以及性别与L1 - ACH之间的交互作用（L1×L1潜在交互作用）并不显著。尽管随机斜率模型显示L1 - ACH与L1 - ASC之间的关系在学校之间没有显著差异，但L2 - ACH的负面影响（BFLPE）确实会因个体L1 - ACH而有所不同。我们最后阐述了这组潜在情境模型在不同应用中的意义，包括关于其实施的建议、适用于多层模型的效应量估计（及置信区间），以及情境效应分析的进一步研究方向。
