Estimates for geographical domains through geoadditive models in presence of missing information

The implementation of geoadditive models needs the statistical units to be referenced at point locations. If the aim of the study is to analyze the spatial pattern or to produce a spatial interpolation of a studied phenomenon, spatial information are required only for the sampled units. If, however, the geoadditive model is used to produce estimates of a parameter of interest for some geographical domains, the spatial location is required for all the population units. This information is not always easily available. Typically, we know the coordinates for sampled units, but for the non-sampled units we know just the areas - like blocks, municipalities, etc. - to which they belong. In such situation, the classical approach is to locate all the units by the coordinates of their corresponding area centroid. This is obviously an approximation and its effect on the estimates can be strong, depending on the level of nonlinearity in the spatial pattern and on the area dimension. We decided to investigate a different approach: instead of using the same coordinates for all the units, we impose a distribution for the locations inside each area. To analyze the performance of this approach, various MCMC experiments are implemented.