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

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.