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

Alexander Robitzsch
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Alexander Robitzsch: IPN—Leibniz Institute for Science and Mathematics Education, Olshausenstrasse 62, 24118 Kiel, Germany

Mathematics, 2021, vol. 9, issue 13, 1-17

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.

Keywords: latent D-scoring model; logistic item response model; identifiability; item parameter estimation; PISA (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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