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Modeling Differences Between Response Times of Correct and Incorrect Responses

Published online by Cambridge University Press:  01 January 2025

Maria Bolsinova  and
Jesper Tijmstra
Maria Bolsinova*
Affiliation:
ACTNext
Jesper Tijmstra
Affiliation:
Tilburg University
*
Correspondence should be made to Maria Bolsinova, ACTNext, 500 ACT dr., Iowa City, IA 52243, USA. Email:[email protected]
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Abstract

While standard joint models for response time and accuracy commonly assume the relationship between response time and accuracy to be fully explained by the latent variables of the model, this assumption of conditional independence is often violated in practice. If such violations are present, taking these residual dependencies between response time and accuracy into account may both improve the fit of the model to the data and improve our understanding of the response processes that led to the observed responses. In this paper, we propose a framework for the joint modeling of response time and accuracy data that allows for differences in the processes leading to correct and incorrect responses. Extensions of the standard hierarchical model (van der Linden in Psychometrika 72:287–308, 2007. https://doi.org/10.1007/s11336-006-1478-z) are considered that allow some or all item parameters in the measurement model of speed to differ depending on whether a correct or an incorrect response was obtained. The framework also allows one to consider models that include two speed latent variables, which explain the patterns observed in the responses times of correct and of incorrect responses, respectively. Model selection procedures are proposed and evaluated based on a simulation study, and a simulation study investigating parameter recovery is presented. An application of the modeling framework to empirical data from international large-scale assessment is considered to illustrate the relevance of modeling possible differences between the processes leading to correct and incorrect responses.

Keywords

conditional dependencehierarchical modeljoint modelingresponse times
Type
Original Paper
Information
Psychometrika , Volume 84 , Issue 4 , December 2019 , pp. 1018 - 1046
Copyright
Copyright © 2019 The Psychometric Society

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Footnotes

Electronic supplementary materialThe online version of this article (https://doi.org/10.1007/s11336-019-09682-5) contains supplementary material, which is available to authorized users.

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