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Two Interpretations of the Discrimination Parameter

Published online by Cambridge University Press:  01 January 2025

Francis Tuerlinckx  and
Paul De Boeck
Francis Tuerlinckx*
Affiliation:
Department of Psychology, University of Leuven
Paul De Boeck
Affiliation:
Department of Psychology, University of Leuven
*
Requests for reprints should be sent to to Francis Tuerlinckx, Department of Psychology, University of Leuven, Tiensestraat 102, B-3000 Leuven, Belgium. E-mail: francis.tuerlinckx@psy.kuleuven.be
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Abstract

In this paper we propose two interpretations for the discrimination parameter in the two-parameter logistic model (2PLM). The interpretations are based on the relation between the 2PLM and two stochastic models. In the first interpretation, the 2PLM is linked to a diffusion model so that the probability of absorption equals the 2PLM. The discrimination parameter is the distance between the two absorbing boundaries and therefore the amount of information that has to be collected before a response to an item can be given. For the second interpretation, the 2PLM is connected to a specific type of race model. In the race model, the discrimination parameter is inversely related to the dependency of the information used in the decision process. Extended versions of both models with person-to-person variability in the difficulty parameter are considered. When fitted to a data set, it is shown that a generalization of the race model that allows for dependency between choices and response times (RTs) is the best-fitting model.

Keywords

item response theoryitem discriminationtwo-parameter logistic modeldiffusion modelrace modelresponse times
Type
Theory and Methods
Information
Psychometrika , Volume 70 , Issue 4 , December 2005 , pp. 629 - 650
Copyright
Copyright © 2005 The Psychometric Society

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