Estimating Identification Disclosure Risk Using Mixed Membership Models

• Activity Number: 8
• Type: Invited
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Government Statistics
• Author(s): Daniel Manrique-Vallier*+ and Jerome P Reiter
• Companies: Duke University and Duke University
• Keywords: Contingency table ; Confidentiality ; Disclosure ; Grade of Membership ; Mixed Membership ; log-linear models

Abstract

Statistical agencies and other organizations that disseminate data are obligated to protect data subjects' confidentiality. Even apparently safe "anonymized" datasets pose disclosure risks for individuals whose characteristics are sufficiently atypical. Hence, as part of their assessments of disclosure risks, many data stewards estimate the probabilities that sample uniques on sets of discrete key variables are also population uniques on those keys. This is typically done using log-linear modeling on the keys. However, log-linear models can yield biased estimates of cell probabilities for sparse contingency tables with many zero counts, which often occurs in databases with many keys. This bias can result in unreliable estimates of probabilities of uniqueness and, hence, misrepresentations of disclosure risks. We propose an alternative to log-linear models for datasets with sparse keys based on a Bayesian version of grade of membership (GoM) models. In our analyses, GoM models provide more accurate estimates of the total number of uniques in the samples, and they offer record-level predictions of uniqueness that dominate those based on log-linear models.