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About the Equivalence of the Latent D-Scoring Model and the Two-Parameter Logistic Item Response Model

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  • Alexander Robitzsch

    (IPN—Leibniz Institute for Science and Mathematics Education, Olshausenstrasse 62, 24118 Kiel, Germany
    Centre for International Student Assessment (ZIB), Olshausenstrasse 62, 24118 Kiel, Germany)

Abstract

This article shows that the recently proposed latent D-scoring model of Dimitrov is statistically equivalent to the two-parameter logistic item response model. An analytical derivation and a numerical illustration are employed for demonstrating this finding. Hence, estimation techniques for the two-parameter logistic model can be used for estimating the latent D-scoring model. In an empirical example using PISA data, differences of country ranks are investigated when using different metrics for the latent trait. In the example, the choice of the latent trait metric matters for the ranking of countries. Finally, it is argued that an item response model with bounded latent trait values like the latent D-scoring model might have advantages for reporting results in terms of interpretation.

Suggested Citation

  • Alexander Robitzsch, 2021. "About the Equivalence of the Latent D-Scoring Model and the Two-Parameter Logistic Item Response Model," Mathematics, MDPI, vol. 9(13), pages 1-17, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1465-:d:580050
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    References listed on IDEAS

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    1. Dale Ballou, 2009. "Test Scaling and Value-Added Measurement," Education Finance and Policy, MIT Press, vol. 4(4), pages 351-383, October.
    2. James A Wiley & John Levi Martin & Stephen J Herschkorn & Jason Bond, 2015. "A New Extension of the Binomial Error Model for Responses to Items of Varying Difficulty in Educational Testing and Attitude Surveys," PLOS ONE, Public Library of Science, vol. 10(11), pages 1-16, November.
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