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

The paper deals with the matter of producing geographical domains estimates for a variable with a spatial pattern in presence of incomplete information about the population units location. The spatial distribution of the study variable and its eventual relations with other covariates are modeled by a geoadditive regression. The use of such a model to produce model-based estimates for some geographical domains requires all the population units to be referenced at point locations, however typically the spatial coordinates are known only for the sampled units. An approach to treat the lack of geographical information for non-sampled units is suggested: it is proposed to impose a distribution on the spatial locations inside each domain. This is realized through a hierarchical Bayesian formulation of the geoadditive model in which a prior distribution on the spatial coordinates is defined. The performance of the proposed imputation approach is evaluated through various Markov Chain Monte Carlo experiments implemented under different scenarios.