There is an extensive and continuing concern over the human health effects of air pollutants. In this work, motivated by a case study on daily hospitalizations for cardiovascular and respiratory diseases in Piemonte and Lombardia regions (Italy), we introduce a Bayesian spatial factor augmented vector autoregressive (S-FAVAR) model to study the spatial and temporal association existing between health data and air pollution.

The model is developed for handling measurements belonging to the exponential family of distributions and allow the spatial and temporal components to be modeled conditionally independently via a latent factor analysis structure for the (canonical) transformation of the measurements mean function.

The proposed model has an intuitive appeal and enjoys several advantages. For example, it describes the spatial-temporal variability of the diseas risk and explicitly defines a non-separable spatio-temporal covariance structure of the process. Also, it allows to study how the disease risk at a specific areal unit reacts over time to exogenous impulses from the same or different areal units. Finally, several general structures that make use of different covariate information, can be easily accommodated in the different levels of the hierarchy.

The S-FAVAR model is developed within a state-space framework and full probabilistic inference for the parameters is facilitated by a Markov chain Monte Carlo (MCMC) scheme for multivariate dynamic systems.