A Compensatory Approach to Optimal Selection with Mastery Scores. Research Report 94-2

This paper presents some Bayesian theories of simultaneous optimization of decision rules for test-based decisions. Simultaneous decision making arises when an institution has to make a series of selection, placement, or mastery decisions with respect to subjects from a population. An obvious exampl...

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Bibliographic Details
Main Authors van der Linden, Wim J, Vos, Hans J
Format Report
LanguageEnglish
Published Bibliotheek, Faculty of Educational Science and Technology, University of Twente 01.11.1994
Subjects
Bayesian Statistics
Compensatory Models
Decision Making
Decision Rules
Foreign Countries
Mastery Model
Scores
Scoring
Selection
Simultaneous Processing
Test Items
Utility Functions
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Summary:This paper presents some Bayesian theories of simultaneous optimization of decision rules for test-based decisions. Simultaneous decision making arises when an institution has to make a series of selection, placement, or mastery decisions with respect to subjects from a population. An obvious example is the use of individualized instruction in education. Compared with separate optimization, a simultaneous approach has two advantages. First, test scores used in previous decisions can be used as "prior" data in later decisions, and the efficiency of the decisions can be increased. Second, more realistic utility structures can be obtained defining utility functions for earlier decisions on later criteria. An important distinction is made between weak and strong decision rules. As opposed to strong rules, weak rules are allowed to be a function of prior test scores. Conditions for monotonicity of optimal weak and strong rules are presented. Also, it is shown that under mild conditions on the test score distributions and utility functions, weak rules are always compensatory by nature. To illustrate this approach, a common decision problem in education and psychology, consisting of a selection decision for treatment followed by a mastery decision, is analyzed. (Contains 1 figure, 2 tables, and 23 references.) (Author)