Penalized small area models for the combination of unit- and area-level data

The joint usage of unit- and area-level data for model-based small area estimation is investigated. The combination of levels within a single model encloses a variety of methodological problems. Firstly, it implies a critical decrease in degrees of freedom due to more model parameters that need to be estimated. This may destabilize model predictions in the presence of small samples. Secondly, unit- and area-level data has different distributional characteristics in terms of dispersion patterns and correlation structure. Thirdly, unit- and area-level data is usually subject to different kinds of measurement errors. We propose a multi-level model with level-specific penalization to overcome these issues and use unit- and area-level data jointly for model-based small area estimation. An application is provided on the example of regional health measurement in Germany. We combine health survey data on the unit-level and aggregated micro census records on the area-level to estimate hypertension prevalence.