2016/02/22 by Silvia Liverani, Aurore Lavigné, Liverani, Silvia +4 · 2 citations
Economics, Econometrics and Finance · Environmental Science · Mathematics · Social Sciences · #Air Quality and Health Impacts #Applications (stat.AP) #Bayesian probability #Collinearity #Computer science #Confounding #Correlation #Covariate #Econometrics #Economic and Environmental Valuation #Environmental Justice and Health Disparities #FOS: Computer and information sciences #Index (typography) #Mathematics #Regression #Regression analysis #Spatial correlation #Statistics #stat.AP
paper · pdf · open access · doi:10.48550/arxiv.1602.06972
published in arXiv (Cornell University) (Cornell University)
arxiv created 2016/02/22 · openalex publication_date 2016/02/22 · arxiv updated 2016/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.