LinearModels Decomposition of Prediction Error in Multilevel Models

We present a decomposition of prediction error for the multilevel model in the context of predicting a future observable y∗j in the jth group of a hierarchical dataset. The multilevel prediction rule is used for prediction and the components of prediction error are estimated via a simulation study that spans the various combinations of level-1 (individual) and level-2 (group) sample sizes and different intraclass correlation values. Additionally, analytical results present the increase in predicted mean square error (PMSE) with respect to prediction error bias. The components of prediction error provide information with respect to the cost of parameter estimation versus data imputation for predicting future values in a hierarchical data set. Specifically, the cost of parameter estimation is very small compared to data imputation.