An Expanded Decision-Making Procedure for Examining Cross-Level Interaction Effects With Multilevel Modeling
提出新的组内相关系数ρβ，用于评估低层结果变量方差中由高层斜率差异解释的部分，并建议研究者在使用多层模型时同时考虑传统组内相关系数ρα和ρβ，以更全面判断数据非独立性。
Cross-level interaction effects lay at the heart of multilevel contingency and interactionism theories. Also, practitioners are particularly interested in such effects because they provide information on the contextual conditions and processes under which interventions focused on individuals (e.g., selection, leadership training, performance appraisal, and management) result in more or less positive outcomes. We derive a new intraclass correlation, ρ β , to assess the degree of lower-level outcome variance that is attributed to higher-level differences in slope coefficients. We provide analytical and empirical evidence that ρ β is an index of variance that differs from the traditional intraclass correlation ρ α and use data from recently published articles to illustrate that ρ α assesses differences across collectives and higher-level processes (e.g., teams, leadership styles, reward systems) but ignores the variance attributed to differences in lower-level relationships (e.g., individual level job satisfaction and individual level performance). Because ρ α and ρ β provide information on two different sources of variability in the data structure (i.e., differences in means and differences in relationships, respectively), our results suggest that researchers contemplating the use of multilevel modeling, as well those who suspect nonindependence in their data structure, should expand the decision criteria for using multilevel approaches to include both types of intraclass correlations. To facilitate this process, we offer an illustrative data set and the icc beta R package for computing ρ β in single- and multiple-predictor situations and make them available through the Comprehensive R Archive Network (i.e., CRAN).