The Extended Crosswise Model Adjusted for Random Answering

Abstract The Extended Crosswise Model is a popular randomized response design that employs a sensitive and innocuous statement, and asks respondents if one of these statements is true, or if none or both are true. Although the model has a degree of freedom, it is unable to detect random answering. In this article, we propose a new method to detect and correct for random answering. This method makes use of a non-sensitive control statement and a quasi-randomized innocuous statement to which both answers are known, which allows for the detection of and correction for random answering. A simulation study shows that this method yields unbiased estimates of the prevalence of sensitive attribute. For four surveys among elite athletes, we present prevalence estimates of doping use that are corrected for random answering.