A Multivariate Randomized Response Model for Sensitive Binary Data

Abstract

A new statistical method is proposed to combine the randomized response technique, probit modeling, and Bayesian analysis to analyze large-scale online surveys of multiple binary randomized responses. The proposed method is illustrated by analyzing sensitive dichotomous randomized responses on different types of drug administration error from nurses in a hospital cluster. A statistical challenge is that nurses’ true sensitive responses are unobservable because of a randomization scheme that protects their data privacy to answer the sensitive questions. Four main contributions of the paper are highlighted. The first is the construction of a generic statistical approach in modeling multivariate sensitive binary data collected from the randomized response technique. The second is studying the dependence of multivariate sensitive responses via statistical measures. The third is the calculation of an overall attitude score using sensitive responses. The last one is an illustration of the proposed statistical method for analyzing administration policies that potentially involve sensitive topics which are important to study but are not easily investigated via empirical studies. The particular healthcare example on drug administration policies demonstrated in this paper also presents a scientific way to elicit managerial strategies while protecting data privacy through analytics.