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A Mixture Cure-Rate Model for Responses and Response Times in Time-Limit Tests

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  • Yi-Hsuan Lee
  • Zhiliang Ying

Abstract

Many large-scale standardized tests are intended to measure skills related to ability rather than the rate at which examinees can work. Time limits imposed on these tests make it difficult to distinguish between the effect of low proficiency and the effect of lack of time. This paper proposes a mixture cure-rate model approach to address this issue. Maximum likelihood estimation is proposed for parameter and variance estimation for three cases: when examinee parameters are to be estimated given precalibrated item parameters, when item parameters are to be calibrated given known examinee parameters, and when item parameters are to be estimated without assuming known examinee parameters. Large-sample properties are established for the cases under suitable regularity conditions. Simulation studies suggest that the proposed approach is appropriate for inferences concerning model parameters. In addition, not distinguishing between the effect of low proficiency and the effect of lack of time is shown to have considerable consequences for parameter estimation. A real data example is presented to demonstrate the new model. Choice of survival models for the latent power times is also discussed. Copyright The Psychometric Society 2015

Suggested Citation

  • Yi-Hsuan Lee & Zhiliang Ying, 2015. "A Mixture Cure-Rate Model for Responses and Response Times in Time-Limit Tests," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 748-775, September.
    • Handle: RePEc:spr:psycho:v:80:y:2015:i:3:p:748-775
    DOI: 10.1007/s11336-014-9419-8
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    References listed on IDEAS

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    6. Gunter Maris & Han Maas, 2012. "Speed-Accuracy Response Models: Scoring Rules based on Response Time and Accuracy," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 615-633, October.
    7. Gerard Breukelen, 2005. "Psychometric Modeling of response speed and accuracy with mixed and conditional regression," Psychometrika, Springer;The Psychometric Society, vol. 70(2), pages 359-376, June.
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    9. Johnson, Matthew S., 2007. "Marginal Maximum Likelihood Estimation of Item Response Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i10).
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    Cited by:

    1. Jinxin Guo & Xin Xu & Zhiliang Ying & Susu Zhang, 2022. "Modeling Not-Reached Items in Timed Tests: A Response Time Censoring Approach," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 835-867, September.

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