Modelling collinear and spatially correlated data - Liverani,S; Lavigne,A; Blangiardo,MAG (Spatial and Spatio-temporal Epidemiology, 2016)
In this work we present a statistical approach to distinguish and interpret the complexrelationship between several predictors and a response variable at the small area level, in thepresence of i) high correlation between the predictors and ii) spatial correlation for the response.Covariates which are highly correlated create collinearity problems when used in a standardmultiple regression model. Many methods have been proposed in the literature to address thisissue. A very common approach is to create an index which aggregates all the highly correlatedvariables of interest. For example, it is well known that there is a relationship between socialdeprivation measured through the Multiple Deprivation Index (IMD) and air pollution; thisindex is then used as a confounder in assessing the effect of air pollution on health outcomes(e.g. respiratory hospital admissions or mortality). However it would be more informative tolook specifically at each domain of the IMD and at its relationship with air pollution to betterunderstand its role as a confounder in the epidemiological analyses.In this paper we illustrate how the complex relationships between the domains of IMD and airpollution can be deconstructed and analysed using profile regression, a Bayesian non-parametricmodel for clustering responses and covariates simultaneously. Moreover, we include an intrinsicspatial conditional autoregressive (ICAR) term to account for the spatial correlation of theresponse variable.