A neutral comparative analysis of additive, multiplicative, and mixed quantitative randomized response models

Abstract

In survey sampling, the randomized response technique is a useful tool to collect reliable data in many fields including sociology, education, economics, and psychology etc. Over the past few decades, many variants of quantitative randomized response models have been developed by researchers. The existing literature on randomized response models lacks a neutral comparative study of different models to help the practitioners choose the appropriate model for a given practical problem. In most of the existing studies, the authors tend to show only the favorable results by hiding the cases where their suggested models are inferior to the existing models. This approach often leads to biased comparisons which may badly misguide the practitioners when choosing a randomized response model for a practical problem at hand. This paper attempts a neutral comparison of six existing quantitative randomized response models using separate as well as joint measures of respondent-privacy and model-efficiency. The findings suggest that one model may perform better than the other model in terms of efficiency but may perform worse when other metrics of model quality are taken into account. The current study guides practitioners in choosing the right model for a given problem under a particular situation.