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Refinement of the extended crosswise model with a number sequence randomizer: Evidence from three different studies in the UK

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  • Khadiga H A Sayed
  • Maarten J L F Cruyff
  • Peter G M van der Heijden
  • Andrea Petróczi

Abstract

The Extended Crosswise Model (ECWM) is a randomized response model with neutral response categories, relatively simple instructions, and the availability of a goodness-of-fit test. This paper refines this model with a number sequence randomizer that virtually precludes the possibility to give evasive responses. The motivation for developing this model stems from a strategic priority of WADA (World Anti-Doping Agency) to monitor the prevalence of doping use by elite athletes. For this model we derived a maximum likelihood estimator that allows for binary logistic regression analysis. Three studies were conducted on online platforms with a total of over 6, 000 respondents; two on controlled substance use and one on compliance with COVID-19 regulations in the UK during the first lockdown. The results of these studies are promising. The goodness-of-fit tests showed little to no evidence for response biases, and the ECWM yielded higher prevalence estimates than direct questions for sensitive questions, and similar ones for non-sensitive questions. Furthermore, the randomizer with the shortest number sequences yielded the smallest response error rates on a control question with known prevalence.

Suggested Citation

  • Khadiga H A Sayed & Maarten J L F Cruyff & Peter G M van der Heijden & Andrea Petróczi, 2022. "Refinement of the extended crosswise model with a number sequence randomizer: Evidence from three different studies in the UK," PLOS ONE, Public Library of Science, vol. 17(12), pages 1-19, December.
    • Handle: RePEc:plo:pone00:0279741
    DOI: 10.1371/journal.pone.0279741
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    References listed on IDEAS

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    1. Christian Hopp & Alexander Speil, 2019. "Estimating the extent of deceitful behaviour using crosswise elicitation models," Applied Economics Letters, Taylor & Francis Journals, vol. 26(5), pages 396-400, March.
    2. Jun-Wu Yu & Guo-Liang Tian & Man-Lai Tang, 2008. "Two new models for survey sampling with sensitive characteristic: design and analysis," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(3), pages 251-263, April.
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