Bayesian Estimation Methods for Multidimensional Models for Discrete and Continuous Responses (RR-06-05)
Cees A. W. Glas
University of Twente, Enschede, The Netherlands

Executive Summary

In previous Law School Admission Council reports, models for the combination of discrete (correct versus incorrect) and continuous responses were presented, as was a model that incorporates both the speed and accuracy of responses to test questions (items). Yet another model was presented for comparing grade point averages (GPAs) of students with different but overlapping sets of courses.

In the present report, two new approaches to analyzing such data are developed. First, a comprehensive method is developed that can simultaneously estimate the parameters for a broad class of models incorporating discrete and continuous responses. Second, the model for comparing GPAs is generalized further. This generalization is motivated by the fact that comparisons between GPAs may confound studentsí profiles of proficiencies with their choice of courses. Therefore, the previous model for the GPAs is enhanced with a model for the choice of the courses.

In an empirical study with a dataset from the Dutch national exams taken at the end of secondary education, we demonstrate the use of the two models and compare their results. The parameter in the choice model that was assumed to drive the choice of courses appears to correlate highly with the proficiencies measured by the exams. The correlation is highest for mathematics ability. The mean difficulty parameters for the exams allows us to rank the courses with respect to difficulty. More difficult subjects such as Mathematics and Business Economy tend to be chosen by the more proficient students.

Bayesian Estimation Methods for Multidimensional Models for Discrete and Continuous Responses (RR-06-05)

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