Geoadditive models for unplanned geographical domains

The complexity of spatial data and the intrinsic spatial relationships limit the usefulness of conventional techniques for extracting spatial patterns. Therefore, the area definition and the assignment of the data to appropriate areas can pose problems in the estimation process. Semi-parametric models have been proposed to simultaneously incorporate the spatial distribution of the study variable and the other covariate effects. Geoadditive models, in particular, merge an additive model, that accounts for the relationship between the variables, and a kriging model, that accounts for the spatial distribution, under the linear mixed model framework. The small area estimates are usually based on a combination of sample surveys and administrative data. Moreover, variables can be skewed, thus the relationship between the response variable and the auxiliary variables may not be linear in the original scale, but can be linear in a transformed scale e.g. the logarithm scale. In such case, small area estimation (SAE) methods based on log-transformed models are required. Combining the need of small area estimation methods for skewed variables with the flexibility of a semi-parametric model, we discuss a recent approach to identify and include the spatial pattern in small area estimation using a model-based direct estimator - MBDE