Estimating the dependence of mixed sensitive response types in randomized response technique

Sensitive questions are often involved in healthcare or medical survey research. Much empirical evidence has shown that the randomized response technique is useful for the collection of truthful responses. However, few studies have discussed methods to estimate the dependence of sensitive responses of multiple types. This study aims to fill that gap by considering a method based on moment estimation and without using the joint distribution of the responses. In addition to the construction of a covariance matrix for the multiple sensitive questions despite incomplete information due to the randomized response technique design, we can calculate the conditional mean of continuous sensitive responses given as categorical responses and partial correlations among continuous sensitive responses. We conduct a simulation experiment to study the bias and variance of the moment estimator with various sample sizes. We apply the proposed method in a healthcare study of the dependence structure among the responses of a survey concerning health and pressure on college students.