L2 Aggregates: A Reflection on Reflective Variables in Multilevel Modeling

• In Event: New Insights for Designing Multilevel Models: Predicting Random Effects, Using Predictor Aggregates, and Mediation Planning

Abstract

This paper focuses on instances in which lower-level units (L1) considered to be interchangeable (e.g., students) provide measures of an upper-level (L2) common target variable (e.g., school climate) for the sole purpose of creating a cluster-level predictor (reflective variable). While previous work has shown how L2 aggregate predictor-outcome coefficient estimates can be biased as a function of sampling and measurement error, those results relied on contextual-focused multilevel models that assumed low ICCs; in other words, situations where predictor variables have substantive meaning at both levels of a model, not just L2. We re-evaluate this issue under design conditions better aligned with reflective L2 predictors. In so doing, we show that parameter estimate bias can be much smaller than previously shown.

Authors

• Timothy R. Konold, University of Virginia

• Elizabeth A. Sanders, University of Washington