Bayesian ecological regression with latent factors: athmospheric pollutants emissions and mortality for lung cancer

In this work we propose a Bayesian ecological analysis in which a latent variable summarizes data on emissions of atmospheric pollutants. We specified a hierarchical Bayesian model with spatially structured and unstructured random terms with a nested latent factor model. This can be considered a combination of the convolution spatial model of Besag et al. (1991) and an ecological regression analysis in which a latent variable plays the role of the covariate. The unified approach allows to proper account for the uncertainty in the latent score estimation in the regression analysis. The Bayesian Latent Factor model is used to summarize the information on environmental pressure derived from three stressors: Carbon Monoxide, Nitrogen Oxides and Inhalable Particles. We found evidence of positive correlation between Lung cancer mortality and environmental pressure indicators, in males, Tuscany (Italy), 1995–1999. Environmental pressure seems to be restricted to fourteen municipalities (top 5% of the Latent Factor distribution). The model identified two areas with high point source emissions.