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Modeling Differences Between Response Times of Correct and Incorrect Responses

Author

Listed:
  • Maria Bolsinova

    (ACTNext)

  • Jesper Tijmstra

    (Tilburg University)

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.

Suggested Citation

  • Maria Bolsinova & Jesper Tijmstra, 2019. "Modeling Differences Between Response Times of Correct and Incorrect Responses," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 1018-1046, December.
  • Handle: RePEc:spr:psycho:v:84:y:2019:i:4:d:10.1007_s11336-019-09682-5
    DOI: 10.1007/s11336-019-09682-5
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    References listed on IDEAS

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    1. Wim J. van der Linden, 2006. "A Lognormal Model for Response Times on Test Items," Journal of Educational and Behavioral Statistics, , vol. 31(2), pages 181-204, June.
    2. Jeffrey Rouder & Dongchu Sun & Paul Speckman & Jun Lu & Duo Zhou, 2003. "A hierarchical bayesian statistical framework for response time distributions," Psychometrika, Springer;The Psychometric Society, vol. 68(4), pages 589-606, December.
    3. Maria Bolsinova & Jesper Tijmstra, 2016. "Posterior Predictive Checks for Conditional Independence Between Response Time and Accuracy," Journal of Educational and Behavioral Statistics, , vol. 41(2), pages 123-145, April.
    4. Wim Linden & Cees Glas, 2010. "Statistical Tests of Conditional Independence Between Responses and/or Response Times on Test Items," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 120-139, March.
    5. Wim van der Linden, 2007. "A Hierarchical Framework for Modeling Speed and Accuracy on Test Items," Psychometrika, Springer;The Psychometric Society, vol. 72(3), pages 287-308, September.
    6. Chun Wang & Zhewen Fan & Hua-Hua Chang & Jeffrey A. Douglas, 2013. "A Semiparametric Model for Jointly Analyzing Response Times and Accuracy in Computerized Testing," Journal of Educational and Behavioral Statistics, , vol. 38(4), pages 381-417, August.
    7. Maria Bolsinova & Paul Boeck & Jesper Tijmstra, 2017. "Modelling Conditional Dependence Between Response Time and Accuracy," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1126-1148, December.
    8. R. Klein Entink & J.-P. Fox & W. Linden, 2009. "A Multivariate Multilevel Approach to the Modeling of Accuracy and Speed of Test Takers," Psychometrika, Springer;The Psychometric Society, vol. 74(1), pages 21-48, March.
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    10. James H. Albert, 1992. "Bayesian Estimation of Normal Ogive Item Response Curves Using Gibbs Sampling," Journal of Educational and Behavioral Statistics, , vol. 17(3), pages 251-269, September.
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