An Application of Multilevel Model Prediction to Nels:88

Multilevel modeling is often used in the social sciences for analyzing data that has a hierarchical structure, e.g., students nested within schools. In an earlier study, we investigated the performance of various prediction rules for predicting a future observable within a hierarchical data set (Afshartous & de Leeuw, 2004). We apply the multilevel prediction approach to the NELS:88 educational data in order to assess the predictive performance on a real data set; four candidate models are considered and predictions are evaluated via both cross-validation and bootstrapping methods. The goal is to develop model selection criteria that assess the predictive ability of candidate multilevel models. We also introduce two plots that 1) aid in visualizing the amount to which the multilevel model predictions are “shrunk” or translated from the OLS predictions, and 2) help identify if certain groups exist for which the predictions are particularly good or bad.