A multivariate randomized response model for mixed-type data

It is not uncommon for surveys in the social sciences to ask sensitive questions. Asking sensitive questions indirectly enables collecting of the desirable sensitive information while at the same time protecting respondents' data privacy. The randomized response technique, which uses a randomization scheme to collect sensitive responses, is one common approach used to achieve this. In this paper, we propose a multivariate ordered probit model to jointly analyze binary and ordinal sensitive response variables. We also develop Bayesian methods to estimate the probit model and perform posterior inference. The proposed probit model is applied to a large-scale drug administration survey to understand the work practice and experience of staff in three hospitals in Hong Kong. Randomized response technique was adopted in this drug administration survey to maintain the anonymity of staff whose work practice may deviate from official hospital guidelines. Empirical results using the drug administration data illustrate that we can understand the experience and practice of staff members in giving medication through probit modeling. Knowing the staff's practice on giving medication can indicate what drug administration procedures the staff may not follow properly and what areas to focus on for the enhancing of drug administration.