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Estimating the prevalence of sensitive behaviour and cheating with a dual design for direct questioning and randomized response


  • Ardo van den Hout
  • Ulf Böckenholt
  • Peter G. M. van der Heijden


Randomized response is a misclassification design to estimate the prevalence of sensitive behaviour. Respondents who do not follow the instructions of the design are considered to be cheating. A mixture model is proposed to estimate the prevalence of sensitive behaviour and cheating in the case of a dual sampling scheme with direct questioning and randomized response. The mixing weight is the probability of cheating, where cheating is modelled separately for direct questioning and randomized response. For Bayesian inference, Markov chain Monte Carlo sampling is applied to sample parameter values from the posterior. The model makes it possible to analyse dual sample scheme data in a unified way and to assess cheating for direct questions as well as for randomized response questions. The research is illustrated with randomized response data concerning violations of regulations for social benefit. Copyright Journal compilation (c) 2010 Royal Statistical Society.

Suggested Citation

  • Ardo van den Hout & Ulf Böckenholt & Peter G. M. van der Heijden, 2010. "Estimating the prevalence of sensitive behaviour and cheating with a dual design for direct questioning and randomized response," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(4), pages 723-736.
  • Handle: RePEc:bla:jorssc:v:59:y:2010:i:4:p:723-736

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    References listed on IDEAS

    1. Jean-Paul Fox, 2005. "Randomized Item Response Theory Models," Journal of Educational and Behavioral Statistics, , vol. 30(2), pages 189-212, June.
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    Cited by:

    1. Korndörfer, Martin & Krumpal, Ivar & Schmukle, Stefan C., 2014. "Measuring and explaining tax evasion: Improving self-reports using the crosswise model," Journal of Economic Psychology, Elsevier, vol. 45(C), pages 18-32.
    2. Liu, Yin & Tian, Guo-Liang, 2013. "A variant of the parallel model for sample surveys with sensitive characteristics," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 115-135.

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