ESTIMATING REGRESSIONS IN m GROUPS

The feasibility of a Bayesian method, due to Lindley, for estimating regressions in m groups is studied by application to data from the Law School Admissions Test Program and the Comparative Guidance Program. Easily computable approximate solutions to the Lindley equations are provided and shown to agree well with the full Bayesian solution in some situations. Numerical investigations are described that lead to the adoption of efficient starting values and an efficient sequencing for the iterative solution of the Lindley equations. The advantages of the Bayesian method over more conventional procedures are discussed. Difficulties encountered by Lindley in the statement of one of his assumptions of independence are investigated and a resolution is found. The validities of other assumptions are checked. Problems arising in the extension of Lindley's method to the multiple correlation case are discussed, and some insight is gained through the use of principal component methods.