Two-Stage Least Squares Analysis of Hierarchical Linear Models

This paper has two major objectives. The first is to present a two-stage least squares procedure for estimation of the parameters in a linear model whose parameters are in themselves linear functions of some hyperparameters. The second, and perhaps more important point, is that the new estimator can be shown to be generally more precise than either the Bayesian or the generalized single-stage least squares estimator reported by LINDLEY and SMITH (1072).