Hierarchical generalised latent spatial quantile regression models with applications to indoor radon concentration

Radon-222 is a noble gas arising naturally from decay of uranium-238 present in the earth's crust. In confined spaces, high concentrations of radon can become a serious health concern. Hence, experts widely agree that prolonged exposure to this gas can significantly increase the risk of lung cancer. A range of variables, such as geological factors, soil properties, building characteristics, the living habits of dwellers and meteorological parameters, might have a significant impact on indoor radon concentration and its variability. In this paper, the effect of various factors that are believed to influence the indoor radon concentrations is studied at the municipal level of L'Aquila district (Abruzzo region, Italy). The statistical analysis is carried out through a hierarchical Bayesian spatial quantile regression model in which the matrix of explanatory variables is partially defined through a set of spatial common latent factors. The proposed model, here referred to as the Generalized latent-spatial-quantile regression model, is thus appropriate when some covariates are indicators of latent factors that can be used as predictors in the quantile regression and the variables are supposed to be spatially correlated. It is shown that the model has an intuitive appeal and that it is preferable when the interest is in studying the effects of covariates on one or both the tails of the response distribution, as in the case of indoor radon concentrations. Full probabilistic inference is performed by applying Markov chain Monte Carlo techniques.