A longitudinal study of the influence of air pollutants on children: a robust multivariate approach

This paper aims to evaluate the statistical association between exposure to air pollution and forced expiratory volume in the first second (FEV₁) in both asthmatic and non-asthmatic children and teenagers, in which the response variable FEV₁ was repeatedly measured on a monthly basis, characterizing a longitudinal experiment. Due to the nature of the data, an robust linear mixed model (RLMM), combined with a robust principal component analysis (RPCA), is proposed to handle the multicollinearity among the covariates and the impact of extreme observations (high levels of air contaminants) on the estimates. The Huber and Tukey loss functions are considered to obtain robust estimators of the parameters in the linear mixed model (LMM). A finite sample size investigation is conducted under the scenario where the covariates follow linear time series models with and without additive outliers (AO). The impact of the time-correlation and the outliers on the estimates of the fixed effect parameters in the LMM is investigated. In the real data analysis, the robust model strategy evidenced that RPCA exhibits three principal component (PC), mainly related to relative humidity (Hmd), particulate matter with a diameter smaller than 10 μm (PM₁₀) and particulate matter with a diameter smaller than 2.5 μm (PM_2.5).