In this work we present a statistical approach to distinguish and interpret the complex
relationship between several predictors and a response variable at the small area level, in the
presence 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 standard
multiple regression model. Many methods have been proposed in the literature to address this
issue. A very common approach is to create an index which aggregates all the highly correlated
variables of interest. For example, it is well known that there is a relationship between social
deprivation measured through the Multiple Deprivation Index (IMD) and air pollution; this
index 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 to
look specifically at each domain of the IMD and at its relationship with air pollution to better
understand its role as a confounder in the epidemiological analyses.
In this paper we illustrate how the complex relationships between the domains of IMD and air
pollution can be deconstructed and analysed using profile regression, a Bayesian non-parametric
model for clustering responses and covariates simultaneously. Moreover, we include an intrinsic
spatial conditional autoregressive (ICAR) term to account for the spatial correlation of the
response variable.