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Bayesian Inference and the Classical Test Theory Model. II Validity and Prediction NICHD CGP LSAT

Jackson, Paul H.; Novick, Melvin R.; Thayer, Dorothy T.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
National Institute for Child Health and Human Development (NICHD), Comparative Guidance and Placement Program (CGP), Educational Counseling, Law School Admission Test (LSAT), Mathematical Applications, Psychometrics, Statistical Analysis, Test Theory, Test Validity


The feasibility and efficacy of a Bayesian method, due to Lindley, for estimating regressions in m groups is studied by application to data from the Law School Admission Test program and the Comparative Guidance program. Easily computable asymptotic solutions to the Lindley equations are provided and shown to approximate well 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.

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