Logistic Regression with Variables Subject to Post Randomization Method

An increase in quality and detail of publicly available databases increases the risk of disclosure of sensitive personal information contained in such databases. The goal of Statistical Disclosure Control (SDC) is to develop methodology that aims at minimizing disclosure risk while providing society with as much information as possible needed for valid statistical inference. The Post Randomization Method (PRAM) is a disclosure avoidance method, where values of categorical variables are perturbed via some known probability mechanism, and only the perturbed data are released thus raising issues regarding disclosure risk and data utility. In this paper, we propose a number of EM algorithms to obtain unbiased estimates of the logistic regression model with data subject to PRAM, and thus effectively account for the effects of PRAM and preserve data utility. The effect of the level of perturbation and sample size on the estimates are evaluated, and relevant standard error estimates are proposed.