IDEAS home Printed from https://ideas.repec.org/a/sae/jedbes/v34y2009i3p378-394.html
   My bibliography  Save this article

A Bivariate Lognormal Response-Time Model for the Detection of Collusion Between Test Takers

Author

Listed:
  • Wim J. van der Linden

Abstract

A bivariate lognormal model for the distribution of the response times on a test by a pair of test takers is presented. As the model has parameters for the item effects on the response times, its correlation parameter automatically corrects for the spuriousness in the observed correlation between the response times of different test takers because of variation in the time intensities of the items. This feature suggests using the model in a routine check of response-time patterns for possible collusion between test takers using an estimate of the correlation parameter or a statistical test of a hypothesis about it. Closed-form expressions for the maximum-likelihood estimations of the model parameters and a Lagrange multiplier test for the correlation parameter are presented. As in any type of statistical decision making, results from such procedures should be corroborated by evidence from other sources, for example, results from a response-based analysis or observations during the test session. The effectiveness of the model in removing the spuriousness from correlated response times is illustrated using empirical response-time data.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:jedbes:v:34:y:2009:i:3:p:378-394
    DOI: 10.3102/1076998609332107
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.3102/1076998609332107
    Download Restriction: no
    File URL: https://libkey.io/10.3102/1076998609332107?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
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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).
    3. Cees Glas, 1999. "Modification indices for the 2-PL and the nominal response model," Psychometrika, Springer;The Psychometric Society, vol. 64(3), pages 273-294, September.
    4. Wim Linden & Fanmin Guo, 2008. "Bayesian Procedures for Identifying Aberrant Response-Time Patterns in Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 73(3), pages 365-384, September.
    Full references (including those not matched with items on IDEAS)

    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. 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. 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.
    3. Edison M. Choe & Jinming Zhang & Hua-Hua Chang, 2018. "Sequential Detection of Compromised Items Using Response Times in Computerized Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 650-673, September.
    4. Steffi Pohl & Esther Ulitzsch & Matthias Davier, 2019. "Using Response Times to Model Not-Reached Items due to Time Limits," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 892-920, September.
    5. 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).
    6. 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.
    7. Hyeon-Ah Kang, 2023. "Sequential Generalized Likelihood Ratio Tests for Online Item Monitoring," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 672-696, June.
    8. 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.
    9. 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.
    10. Renske E. Kuijpers & Ingmar Visser & Dylan Molenaar, 2021. "Testing the Within-State Distribution in Mixture Models for Responses and Response Times," Journal of Educational and Behavioral Statistics, , vol. 46(3), pages 348-373, June.
    11. Onur Demirkaya & Ummugul Bezirhan & Jinming Zhang, 2023. "Detecting Item Preknowledge Using Revisits With Speed and Accuracy," Journal of Educational and Behavioral Statistics, , vol. 48(4), pages 521-542, August.
    12. Hongyue Zhu & Hong Jiao & Wei Gao & Xiangbin Meng, 2023. "Bayesian Change-Point Analysis Approach to Detecting Aberrant Test-Taking Behavior Using Response Times," Journal of Educational and Behavioral Statistics, , vol. 48(4), pages 490-520, August.
    13. 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.
    14. 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.
    15. Yue Liu & Hongyun Liu, 2021. "Detecting Noneffortful Responses Based on a Residual Method Using an Iterative Purification Process," Journal of Educational and Behavioral Statistics, , vol. 46(6), pages 717-752, December.
    16. Matthias von Davier & Lale Khorramdel & Qiwei He & Hyo Jeong Shin & Haiwen Chen, 2019. "Developments in Psychometric Population Models for Technology-Based Large-Scale Assessments: An Overview of Challenges and Opportunities," Journal of Educational and Behavioral Statistics, , vol. 44(6), pages 671-705, December.
    17. A. Béguin & C. Glas, 2001. "MCMC estimation and some model-fit analysis of multidimensional IRT models," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 541-561, December.
    18. Steven Andrew Culpepper & James Joseph Balamuta, 2017. "A Hierarchical Model for Accuracy and Choice on Standardized Tests," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 820-845, September.
    19. Inhan Kang & Paul Boeck & Roger Ratcliff, 2022. "Modeling Conditional Dependence of Response Accuracy and Response Time with the Diffusion Item Response Theory Model," Psychometrika, Springer;The Psychometric Society, vol. 87(2), pages 725-748, June.
    20. Chun Wang, 2015. "On Latent Trait Estimation in Multidimensional Compensatory Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 428-449, June.

    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:sae:jedbes:v:34:y:2009:i:3:p:378-394. 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: SAGE Publications (email available below). General contact details of provider: .

    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.