A new privacy-protecting survey design for multichotomous sensitive variables

Abstract

In this paper, we propose the diagonal model (DM), a survey technique for multicategorical sensitive variables. The DM is a nonrandomized response method; that is, the DM avoids the use of any randomization device. Thus, both survey complexity and study costs are reduced. The DM does not require that at least one outcome of the sensitive variable is nonsensitive. Thus, the model can even be applied to characteristics like income which are sensitive as a whole. We describe the maximum likelihood estimation for the distribution of the sensitive variable and show that the EM algorithm is beneficial to calculate the estimates. Subsequently, we present asymptotic as well as bootstrap confidence intervals. Applying properties of circulant matrices, we show the connection between efficiency loss and the degree of privacy protection (DPP). Here, we prove that the efficiency loss has a lower bound that depends on the DPP. Moreover, for any desired DPP, we derive model parameters that ensure the largest possible efficiency.