Modeling Evasive Response Bias in Randomized Response: Cheater Detection Versus Self-protective No-Saying

Randomized response is an interview technique for sensitive questions designed to eliminate evasive response bias. Since this elimination is only partially successful, two models have been proposed for modeling evasive response bias: the cheater detection model for a design with two sub-samples with different randomization probabilities and the self-protective no sayers model for a design with multiple sensitive questions. This paper shows the correspondence between these models, and introduces models for the new, hybrid "ever/last year" design that account for self-protective no saying and cheating. The model for one set of ever/last year questions has a degree of freedom that can be used for the inclusion of a response bias parameter. Models with multiple degrees of freedom are introduced for extensions of the design with a third randomized response question and a second set of ever/last year questions. The models are illustrated with two surveys on doping use. We conclude with a discussion of the pros and cons of the ever/last year design and its potential for future research.