X matters too: How the blended slope problem manifests differently in unilevel vs. multilevel models

Aside from multilevel models (MLMs), several analytic approaches are available for handling cluster-induced dependencies. Nevertheless, the literature on MLM alternatives has called less explicit attention to the potential bias in level-1 (L1) slope coefficients resulting from the “blended slope” problem—a problem that arises when dependencies in predictors (Xs) exist and when L1 predictor-outcome (X-Y) relations differ from those at level-2 (L2). As such, applied researchers may be drawing incorrect inferences about their L1 predictor effects when they specify models without considering clustering in Xs. The present paper reviews this “blended slope” problem and uses Monte Carlo simulation to illustrate how the problem manifests more for unilevel models compared with MLMs. In short, analyses of clustered data should always: 1) report outcome and predictor ICCs, 2) cluster-mean center L1 predictors or incorporate L2 aggregate predictors, and 3) employ a model that takes clustered residuals into account. peerReviewed publishedVersion

除多层模型（multilevel models, MLMs）外，目前已有多种分析方法可用于处理聚类诱导的相依性问题。然而，现有关于MLMs替代方法的研究文献，却较少明确关注由“混合斜率问题”所引发的第一层（L1）斜率系数潜在偏误——当预测变量（X）存在相依性，且第一层（L1）的预测变量-因变量（X-Y）关联与第二层（L2）的对应关联存在差异时，便会产生该问题。因此，若应用研究者在设定模型时未考虑预测变量X的聚类特征，可能会对其L1预测变量效应作出错误推断。本文对这一“混合斜率问题”展开综述，并通过蒙特卡洛模拟展示：相较于MLMs，单水平模型更易显现该问题。简言之，对聚类数据的分析应始终遵循以下三项原则：1）报告因变量与预测变量的组内相关系数（intraclass correlation coefficients, ICCs）；2）对L1预测变量进行聚类均值中心化处理，或引入第二层（L2）聚合预测变量；3）采用考虑聚类残差的统计模型。经同行评审的已发表版本