Logistic Regression with Variables Subject to Post-Randomization Method

• Activity Number: 125
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Government Statistics
• Author(s): Yong Ming Jeffrey Woo*+ and Aleksandra Slavkovic
• Companies: Penn State University and Penn State University
• Keywords: Statistical disclosure control ; logistic regression ; generalized linear models ; EM algorithm

Abstract

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 provide information in such a way that individual information is sufficiently protected against recognition, while providing society with as much information as possible, and needed for valid statistical inference. One such SDC method is the Post Randomization Method (PRAM), where values of categorical variables are perturbed via some known probability mechanism, and only the perturbed data are being released thus raising issues regarding disclosure risk and data utility. A number of EM algorithms are proposed to obtain unbiased estimates of the logistic regression model after accounting for the effect of PRAM. The effect of the level of perturbation and sample size on the estimates will be evaluated, and relevant standard error estimates will be proposed. The ideas will be extended to generalized linear models.