Prediction in Multilevel Models

Multilevel modeling is an increasingly popular technique for analyzing hierarchical data. This article addresses the problem of predicting a future observable y*j in the jth group of a hierarchical data set. Three prediction rules are considered and several analytical results on the relative performance of these prediction rules are demonstrated. In addition, the prediction rules are assessed by means of a Monte Carlo study that extensively covers both the sample size and parameter space. Specifically, the sample size space concerns the various combinations of level—Level 1 (individual) and Level 2 (group) sample sizes—while the parameter space concerns different intraclass correlation values. The three prediction rules employ OLS, prior, and multilevel estimators for the Level 1 coefficients βj. The multilevel prediction rule performs the best across all design conditions, and the prior prediction rule degrades as the number of groups, J, increases. Finally, this article investigates the robustness of the multilevel prediction rule to misspecifications of the Level 2 model.