Bayesian nonparametric disclosure risk estimation via mixed effects log-linear models

TL;DR

This paper introduces a Bayesian nonparametric approach using Dirichlet process random effects to improve disclosure risk estimation in sparse contingency tables, reducing model complexity while maintaining accuracy.

Contribution

It proposes a novel mixed effects log-linear model with Dirichlet process random effects, enhancing risk estimation reliability and computational efficiency.

Findings

Random effects reduce the need for many fixed effects.

Models with only main effects perform comparably to complex interaction models.

Bayesian approach provides credible intervals and accounts for uncertainty.

Abstract

Statistical agencies and other institutions collect data under the promise to protect the confidentiality of respondents. When releasing microdata samples, the risk that records can be identified must be assessed. To this aim, a widely adopted approach is to isolate categorical variables key to the identification and analyze multi-way contingency tables of such variables. Common disclosure risk measures focus on sample unique cells in these tables and adopt parametric log-linear models as the standard statistical tools for the problem. Such models often have to deal with large and extremely sparse tables that pose a number of challenges to risk estimation. This paper proposes to overcome these problems by studying nonparametric alternatives based on Dirichlet process random effects. The main finding is that the inclusion of such random effects allows us to reduce considerably the number of fixed effects required to achieve reliable risk estimates. This is studied on applications to real data, suggesting, in particular, that our mixed models with main effects only produce roughly equivalent estimates compared to the all two-way interactions models, and are effective in defusing potential shortcomings of traditional log-linear models. This paper adopts a fully Bayesian approach that accounts for all sources of uncertainty, including that about the population frequencies, and supplies unconditional (posterior) variances and credible intervals.