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

Randomized response is a misclassification design to estimate the prevalence of
sensitive behaviour.Respondents who do not followthe 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.