  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.
