A Ratio Estimator for the Mean Using a Mixture Optional Enhance Trust (MOET) Randomized Response Model

When researchers conduct surveys seeking sensitive, socially stigmatized information, respondents, on average, modify their answers to represent themselves favorably. To overcome this issue, researchers may use Randomized Response Technique (RRT) models. Recently, Parker et al. proposed a model that incorporates some of the most critical recent quantitative RRT advancements—mixture, optionality, and enhanced trust—into a single model, which they called a Mixture Optional Enhanced (MOET) model. We now improve upon the MOET model by incorporating auxiliary information into the analysis. Positively correlated auxiliary information can improve the mean response estimation through use of a ratio estimator. In this study, we propose just such an estimator for the MOET model. Further, we investigate the conditions under which the ratio estimator outperforms the basic MOET estimator proposed by Parker et al. in 2024. We also consider the possibility that the collection of auxiliary information may compromise privacy; and we study the impact of privacy reduction on the overall model performance as assessed by the unified measure (UM) proposed by Gupta et al. in 2018.