Assessing Bayesian nonparametric log-linear models: an application to disclosure risk estimation

We present a method for identification of models with good predictive performances in the family of Bayesian log-linear mixed models with Dirichlet process random effects. Such a problem arises in many different applications; here we consider it in the context of disclosure risk estimation, an increasingly relevant issue raised by the increasing demand for data collected under a pledge of confidentiality. Two different criteria are proposed and jointly used via a two-stage selection procedure, in a M-open view. The first stage is devoted to identifying a path of search; then, at the second, a small number of nonparametric models is evaluated through an application-specific score based Bayesian information criterion. We test our method on a variety of contingency tables based on microdata samples from the US Census Bureau and the Italian National Security Administration, treated here as populations, and carefully discuss its features. This leads us to a journey around different forms and sources of bias along which we show that (i) while based on the so called "score+search" paradigm, our method is by construction well protected from the selection-induced bias, and (ii) models with good performances are invariably characterized by an extraordinarily simple structure of fixed effects. The complexity of model selection - a very challenging and difficult task in a strictly parametric context with large and sparse tables - is therefore significantly defused by our approach. An attractive collateral result of our analysis are fruitful new ideas about modeling in small area estimation problems, where interest is in total counts over cells with a small number of observations.