A Note on Equivalent and Nonequivalent Parametrizations of the Two-Parameter Logistic Item Response Model

The two-parameter logistic (2PL) item response model is typically estimated using an unbounded distribution for the trait <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics></ma...

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Bibliographic Details
Main Author: Alexander Robitzsch
Format: Article
Language:English
Published: MDPI AG 2024-10-01
Series:Information
Subjects:
Online Access:https://www.mdpi.com/2078-2489/15/11/668
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Summary:The two-parameter logistic (2PL) item response model is typically estimated using an unbounded distribution for the trait <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics></math></inline-formula>. In this article, alternative specifications of the 2PL models are investigated that consider a bounded or a positively valued <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics></math></inline-formula> distribution. It is highlighted that these 2PL specifications correspond to the partial membership mastery model and the Ramsay quotient model, respectively. A simulation study revealed that model selection regarding alternative ranges of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics></math></inline-formula> distribution can be successfully applied. Different 2PL specifications were additionally compared for six publicly available datasets.
ISSN:2078-2489