Combining Administrative and Survey Data to Correct Coverage Errors in Register-Based Statistics: A Bayesian Approach

The statistical production process of many National Institutes is increasingly exploiting the integration of administrative data and sample surveys. Administrative data are generally affected by errors; among others, under and over-coverage may introduce bias in the statistics produced. In this paper, we propose a method to make inference on the population sizes at different aggregation levels by leveraging administrative data in the presence of coverage errors. We introduce a Bayesian statistical model for integrating nonprobability (register-based) and probability samples. The use of a Bayesian model allows a natural quantification of the uncertainty of estimates through the posterior distribution of the unknown target parameters. Although the framework we discuss is quite general, we will mainly refer to the setting of the Italian Permanent Census. We first assess the model performance using simulated data closely related to the real one; then, we provide results for the real data.