The purpose of this paper is to construct a linear prediction model for a three-stage hierarchical data structure and develop a Bayesian procedure to estimate parameters. More specifically, the regression coefficient vectors in this model are assumed to be exchangeable within a block in the de Finetti's sense, and the block parameters are also assumed to be exchangeable. We employed an E-M algorithm in order to obtain estimates for the hyperparameters of the model. Then, conditional on these estimates, we estimated the rest of the parameters which are relevant for prediction.
Finally, we applied this estimation procedure to the entrance examination data and compared its predictive efficiency with other possible prediction models. We found that the proposed model produced the best root mean squared errors, although the difference from other models was minimal.