On Repeated Measurements in Randomized Response Surveys

Accepted - July 2025

Abstract

Randomization and replication are two basic principles of Statistics. Survey statisticians employ randomized response methods for obtaining the data related to sensitive characteristics. The existing randomized response techniques use the principle of randomization for scrambling the responses of the respondents. The scrambled responses based on one-time surveys may result in large differences between the observed responses and the true responses, thus leading to measurement errors which generally have a negative influence on the estimates of parameters. The existing randomized response methods lack the principle of replication to control for measurement errors. This paper introduces the novel idea of replicating the scrambling process at different time-points using time-scaled surveys. The repeated measurements may balance out the positive and negative measurement errors around the true values, thus resulting in reliable data on sensitive variables. We use weighted moving averages to compare estimators of population mean under time-scaled and traditional surveys. Our findings reveal that the estimates of population mean under time-scaled surveys are more efficient than those based on one-time sample surveys. Additionally, a novel optional scrambling model has been suggested which achieves improvement over the competitor models. A real-world randomized response survey example has also been provided.