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A Semiparametric Model for Jointly Analyzing Response Times and Accuracy in Computerized Testing

Author

Listed:
  • Chun Wang

    (University of Minnesota)

  • Zhewen Fan

    (Precision Therapeutics, Inc.)

  • Hua-Hua Chang

    (University of Illinois at Urbana-Champaign)

  • Jeffrey A. Douglas

Abstract

The item response times (RTs) collected from computerized testing represent an underutilized type of information about items and examinees. In addition to knowing the examinees’ responses to each item, we can investigate the amount of time examinees spend on each item. Current models for RTs mainly focus on parametric models, which have the advantage of conciseness, but may suffer from reduced flexibility to fit real data. We propose a semiparametric approach, specifically, the Cox proportional hazards model with a latent speed covariate to model the RTs, embedded within the hierarchical framework proposed by van der Linden to model the RTs and response accuracy simultaneously. This semiparametric approach combines the flexibility of nonparametric modeling and the brevity and interpretability of the parametric modeling. A Markov chain Monte Carlo method for parameter estimation is given and may be used with sparse data obtained by computerized adaptive testing. Both simulation studies and real data analysis are carried out to demonstrate the applicability of the new model.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:jedbes:v:38:y:2013:i:4:p:381-417
    DOI: 10.3102/1076998612461831
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    References listed on IDEAS

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    1. 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.
    2. Jeffrey Douglas & Michael Kosorok & Betty Chewning, 1999. "A latent variable model for discrete multivariate psychometric waiting times," Psychometrika, Springer;The Psychometric Society, vol. 64(1), pages 69-82, March.
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    Cited by:

    1. Chun Wang & Gongjun Xu & Zhuoran Shang, 2018. "A Two-Stage Approach to Differentiating Normal and Aberrant Behavior in Computer Based Testing," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 223-254, March.
    2. Hua-Hua Chang, 2015. "Psychometrics Behind Computerized Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 1-20, March.
    3. Chen, Haiqin & De Boeck, Paul & Grady, Matthew & Yang, Chien-Lin & Waldschmidt, David, 2018. "Curvilinear dependency of response accuracy on response time in cognitive tests," Intelligence, Elsevier, vol. 69(C), pages 16-23.
    4. 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.

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