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

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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).
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