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Modeling of Responses and Response Times with the Package cirt

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  • Fox, Jean-Paul
  • Entink, Rinke Klein
  • van der Linden, Wilm

Abstract

In computerized testing, the test takers' responses as well as their response times on the items are recorded. The relationship between response times and response accuracies is complex and varies over levels of observation. For example, it takes the form of a tradeoff between speed and accuracy at the level of a fixed person but may become a positive correlation for a population of test takers. In order to explore such relationships and test hypotheses about them, a conjoint model is proposed. Item responses are modeled by a two-parameter normal-ogive IRT model and response times by a lognormal model. The two models are combined using a hierarchical framework based on the fact that response times and responses are nested within individuals. All parameters can be estimated simultaneously using an MCMC estimation approach. A R-package for the MCMC algorithm is presented and explained.

Suggested Citation

  • Fox, Jean-Paul & Entink, Rinke Klein & van der Linden, Wilm, 2007. "Modeling of Responses and Response Times with the Package cirt," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i07).
    • Handle: RePEc:jss:jstsof:v:020:i07
    DOI: http://hdl.handle.net/10.18637/jss.v020.i07
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    References listed on IDEAS

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    1. McCulloch, Robert E. & Polson, Nicholas G. & Rossi, Peter E., 2000. "A Bayesian analysis of the multinomial probit model with fully identified parameters," Journal of Econometrics, Elsevier, vol. 99(1), pages 173-193, November.
    2. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
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    Cited by:

    1. Dylan Molenaar & Paul Boeck, 2018. "Response Mixture Modeling: Accounting for Heterogeneity in Item Characteristics across Response Times," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 279-297, June.
    2. 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.
    3. repec:jss:jstsof:20:i01 is not listed on IDEAS
    4. M. Marsman & H. Sigurdardóttir & M. Bolsinova & G. Maris, 2019. "Characterizing the Manifest Probability Distributions of Three Latent Trait Models for Accuracy and Response Time," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 870-891, September.
    5. Konrad Klotzke & Jean-Paul Fox, 2019. "Modeling Dependence Structures for Response Times in a Bayesian Framework," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 649-672, September.
    6. Shaw, Amy & Elizondo, Fabian & Wadlington, Patrick L., 2020. "Reasoning, fast and slow: How noncognitive factors may alter the ability-speed relationship," Intelligence, Elsevier, vol. 83(C).
    7. Wim J. van der Linden, 2009. "A Bivariate Lognormal Response-Time Model for the Detection of Collusion Between Test Takers," Journal of Educational and Behavioral Statistics, , vol. 34(3), pages 378-394, September.
    8. de Leeuw, Jan & Mair, Patrick, 2007. "An Introduction to the Special Volume on "Psychometrics in R"," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i01).
    9. repec:jss:jstsof:36:c01 is not listed on IDEAS
    10. Hyeon-Ah Kang & Yi Zheng & Hua-Hua Chang, 2020. "Online Calibration of a Joint Model of Item Responses and Response Times in Computerized Adaptive Testing," Journal of Educational and Behavioral Statistics, , vol. 45(2), pages 175-208, April.
    11. 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.
    12. Sukaesi Marianti & Jean-Paul Fox & Marianna Avetisyan & Bernard P. Veldkamp & Jesper Tijmstra, 2014. "Testing for Aberrant Behavior in Response Time Modeling," Journal of Educational and Behavioral Statistics, , vol. 39(6), pages 426-451, December.

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