Repeated Cross-Sectional Randomized Response Data: Taking Design Change and Self-Protective Responses into Account

Randomized response (RR) is an interview technique that can be used to protect the privacy of respondents if sensitive questions are posed. This paper explains how to measure change in time if a binary RR question is posed at several time points. In cross-sectional research settings, new insights often gradually emerge. In our setting, a switch to another RR procedure necessitates the development of a trend model that estimates the effect of the covariate time if the dependent variable is measured by different RR designs. We also demonstrate that it is possible to deal with self-protective responses, thus accommodating our trend model with the latest developments in RR data analysis.