Semiparametric latent variable regression models for spatiotemporal modelling of mobile source particles in the greater Boston area

Summary.  Traffic particle concentrations show considerable spatial variability within a metropolitan area. We consider latent variable semiparametric regression models for modelling the spatial and temporal variability of black carbon and elemental carbon concentrations in the greater Boston area. Measurements of these pollutants, which are markers of traffic particles, were obtained from several individual exposure studies that were conducted at specific household locations as well as 15 ambient monitoring sites in the area. The models allow for both flexible non-linear effects of covariates and for unexplained spatial and temporal variability in exposure. In addition, the different individual exposure studies recorded different surrogates of traffic particles, with some recording only outdoor concentrations of black or elemental carbon, some recording indoor concentrations of black carbon and others recording both indoor and outdoor concentrations of black carbon. A joint model for outdoor and indoor exposure that specifies a spatially varying latent variable provides greater spatial coverage in the area of interest. We propose a penalized spline formulation of the model that relates to generalized kriging of the latent traffic pollution variable and leads to a natural Bayesian Markov chain Monte Carlo algorithm for model fitting. We propose methods that allow us to control the degrees of freedom of the smoother in a Bayesian framework. Finally, we present results from an analysis that applies the model to data from summer and winter separately.