Prediction in Multilevel Models

• Activity Number: 444
• Type: Contributed
• Date/Time: Thursday, August 7, 2003 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Stat. Sciences
• Author(s): David Afshartous*+ and Jan DeLeeuw
• Companies: University of Miami and University of California, Los Angeles
• Keywords: prediction ; Bayes rule ; multilevel model

Abstract

Multilevel modeling is an increasingly popular technique for analyzing hierarchical data. We consider the problem of predicting a future observable $y_{*j}$ in the $j$th group of a hierarchical dataset. We consider three prediction rules and demonstrate several analytical results on the relative performance of these prediction rules. In addition, the prediction rules are assessed via 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-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 $\boldsymbol{\beta}_j$. 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, we investigate the robustness of the Multilevel prediction rule to misspecifications of the level-2 model.