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 hierarchial 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. These components of prediction error provide information with respect to the cost of aparameter estimation versus data inputation for predicting future values in a hierarchial data set. Specifically, the cost of parameter estimation is very small compared to data imputation.