Estimation Quality and Required Sample Sizes in Three-Level Contextual Analysis Models

Authors

  • Denny Kerkhoff Orcid
    Department of Psychology, University of Konstanz, Konstanz, Germany; Department of Psychology, Bielefeld University, Bielefeld, Germany
  • Fridtjof W. Nussbeck Orcid
    Department of Psychology, University of Konstanz, Konstanz, Germany

Abstract

In multilevel analysis, Level-1 predictors that also explain variance at a higher level are called contextual predictors. In the multilevel manifest covariate model, the Level-2 component is modeled as the average of the Level-1 predictor scores within a cluster. In the multilevel latent covariate model, the predictor is decomposed into two latent variables at Level-1 and Level-2. Performance conditions of these modeling approaches for three-level models are largely unexplored. We investigate the two approaches’ performance with respect to bias, coverage, and power in a three-level random intercept model. Results reveal differences in estimation quality and required sample sizes. We provide sampling recommendations for both approaches.