X Matters Too: How the Blended Slope Problem Manifests Differently in Unilevel vs. Multilevel Models

Authors

  • Elizabeth A. Sanders Orcid
    Measurement & Statistics, College of Education, University of Washington, Seattle, WA, USA
  • Timothy R. Konold Orcid
    Research, Statistics, & Evaluation, School of Education and Human Development, University of Virginia, Charlottesville, VA, USA

Abstract

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.