IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v80y2015i3p748-775.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11336-014-9419-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11336-014-9419-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Judy P. Sy & Jeremy M. G. Taylor, 2000. "Estimation in a Cox Proportional Hazards Cure Model," Biometrics, The International Biometric Society, vol. 56(1), pages 227-236, March.
    2. 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.
    3. 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.
    4. Yu-Wei Chang & Rung-Ching Tsai & Nan-Jung Hsu, 2014. "A Speeded Item Response Model: Leave the Harder till Later," Psychometrika, Springer;The Psychometric Society, vol. 79(2), pages 255-274, April.
    5. 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.
    6. Yingwei Peng & Keith B. G. Dear, 2000. "A Nonparametric Mixture Model for Cure Rate Estimation," Biometrics, The International Biometric Society, vol. 56(1), pages 237-243, March.
    7. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 443-459, December.
    8. Wenbin Lu, 2004. "On semiparametric transformation cure models," Biometrika, Biometrika Trust, vol. 91(2), pages 331-343, June.
    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).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tomoyuki Sugimoto & Toshimitsu Hamasaki, 2006. "Properties of estimators of baseline hazard functions in a semiparametric cure model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(4), pages 647-674, December.
    2. Chen, Chyong-Mei & Lu, Tai-Fang C., 2012. "Marginal analysis of multivariate failure time data with a surviving fraction based on semiparametric transformation cure models," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 645-655.
    3. Lu Wang & Pang Du & Hua Liang, 2012. "Two-Component Mixture Cure Rate Model with Spline Estimated Nonparametric Components," Biometrics, The International Biometric Society, vol. 68(3), pages 726-735, September.
    4. Wang, Antai & Zhang, Yilong & Shao, Yongzhao, 2017. "On the likelihood of mixture cure models," Statistics & Probability Letters, Elsevier, vol. 131(C), pages 51-55.
    5. Guoqing Diao & Ao Yuan, 2019. "A class of semiparametric cure models with current status data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 26-51, January.
    6. Ana López-Cheda & Yingwei Peng & María Amalia Jácome, 2023. "Nonparametric estimation in mixture cure models with covariates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 467-495, June.
    7. Sangbum Choi & Xuelin Huang, 2012. "A General Class of Semiparametric Transformation Frailty Models for Nonproportional Hazards Survival Data," Biometrics, The International Biometric Society, vol. 68(4), pages 1126-1135, December.
    8. Mengling Liu & Wenbin Lu & Yongzhao Shao, 2006. "Interval Mapping of Quantitative Trait Loci for Time-to-Event Data with the Proportional Hazards Mixture Cure Model," Biometrics, The International Biometric Society, vol. 62(4), pages 1053-1061, December.
    9. Sandip Barui & Grace Y. Yi, 2020. "Semiparametric methods for survival data with measurement error under additive hazards cure rate models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(3), pages 421-450, July.
    10. Chen, Chyong-Mei & Lu, Tai-Fang C. & Hsu, Chao-Min, 2013. "Association estimation for clustered failure time data with a cure fraction," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 210-222.
    11. Sandip Sinharay & Peter W. van Rijn, 2020. "Assessing Fit of the Lognormal Model for Response Times," Journal of Educational and Behavioral Statistics, , vol. 45(5), pages 534-568, October.
    12. Hanin, Leonid & Huang, Li-Shan, 2014. "Identifiability of cure models revisited," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 261-274.
    13. Luis E. Nieto‐Barajas & Guosheng Yin, 2008. "Bayesian Semiparametric Cure Rate Model with an Unknown Threshold," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 540-556, September.
    14. Suvra Pal & Yingwei Peng & Wisdom Aselisewine, 2024. "A new approach to modeling the cure rate in the presence of interval censored data," Computational Statistics, Springer, vol. 39(5), pages 2743-2769, July.
    15. Yingwei Peng & Jeremy M. G. Taylor, 2017. "Residual-based model diagnosis methods for mixture cure models," Biometrics, The International Biometric Society, vol. 73(2), pages 495-505, June.
    16. Motahareh Parsa & Ingrid Van Keilegom, 2023. "Accelerated failure time vs Cox proportional hazards mixture cure models: David vs Goliath?," Statistical Papers, Springer, vol. 64(3), pages 835-855, June.
    17. Zhang, Jiajia & Peng, Yingwei & Li, Haifen, 2013. "A new semiparametric estimation method for accelerated hazards mixture cure model," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 95-102.
    18. Niu, Yi & Peng, Yingwei, 2014. "Marginal regression analysis of clustered failure time data with a cure fraction," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 129-142.
    19. Yilong Zhang & Xiaoxia Han & Yongzhao Shao, 2021. "The ROC of Cox proportional hazards cure models with application in cancer studies," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(2), pages 195-215, April.
    20. Wenbin Lu, 2008. "Maximum likelihood estimation in the proportional hazards cure model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(3), pages 545-574, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:psycho:v:80:y:2015:i:3:p:748-775. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.