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

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.

Keywords

• hierarchical linear model
• three-level model
• sample sizes
• parameter estimation bias
• power
• coverage
• contextual variable