A Maximin Model for Test Design with Practical Constraints

Wim J. van der Linden · Ellen Boekkooi-Timminga

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Psychometric Methodologies and Testing Educational Assessment and Pedagogy Educational Technology and Assessment

Abstract

A maximin model for IRT-based test design is proposed. In the model only the relative shape of the target test information function is specified. It serves as a constraint subject to which a linear programming algorithm maximizes the information in the test. In the practice of test construction, several demands as linear constraints in the model. A worked example of a text construction problem with practical constraints is presented. The paper concludes with a discussion of some alternative models of test construction.

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References

1969Statistical Theories of Mental Test Scores 1961Probabilistic Models for Some Intelligence and Attainment Tests 2012Applications of Item Response Theory To Practical Testing Problems 1968Some latent trait models and their use in inferring an examinee's ability 1970Principles of Operations Research.2007Applications of Item Response Theory 1985Binary Programming and Test Design

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1998Computer-Assisted Test Assembly Using Optimization Heuristics 1998A Model for Optimal Constrained Adaptive Testing 1998Optimal Assembly of Psychological and Educational Tests 1994Loglinear Multidimensional IRT Models for Polytomously Scored Items 2000Constrained Adaptive Testing with Shadow Tests 1998Methodology Review: Nonparametric IRT Approaches to the Analysis of Dichotomous Item Scores 1990The Construction of Parallel Tests From IRT-Based Item Banks

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