Small area models are mixed effects regression models that link the small areas and borrow strength from similar domains. When the auxiliary variables used in the models are measured with error, small area estimators that ignore the measurement error may be worse than direct estimators. Alternative small area estimators accounting for measurement error have been proposed but only for continuous auxiliary variables. Adopting a Bayesian approach, we plan to extend the unit-level model in order to account for measurement error in both continuous and categorical covariates. However, it is not always straightforward to choose which variables should be considered affected by measurement error: we explore the possibility of modeling the presence of measurement error using specific prior distributions, such as spike-and-slab or global-local shrinking priors. Once the estimates have been obtained, they should be calibrated since model-based estimates from the small areas do not usually match the value of the single estimate for the large area. Benchmarking is done by applying a constraint to ensure that the total of the small areas matches the grand total. We propose two alternative benchmarking strategies: one based on constrained prior distribution and the second one based on sequential Monte Carlo.
The results of the proposed methodologies will be discussed in light of an extensive simulation study and real data applications in demographic and economic context.
A second part of the project will deal with the possibility of calibrating small area models using information coming from two different sources, either survey data or administrative list. In order to tackle this problem we plan to improve and generalize a Bayesian record linkage strategy which is able to account, in a proper way, for the uncertainty due to the linkage step, into the standard error of the estimates of the small area model and of the predictors.
