Por Valdério Anselmo Reisen (Université Paris-Saclay, França and Universidade Federal do Espírito Santo, Brasil).

This study aims to model the statistical relation between exposure to air pollution and forced respiratory volume at the first second (FEV1) in asthmatic and non-asthmatic children, aged up to 18 years. The longitudinal experiment consists of monthly measurements of the response variable FEV1 for each child in Vitória, ES, Brazil. Due to the nature of the data, we propose to combine a robust principal component analysis (RPCA) with a robust estimation of a linear mixed model (LMM) to handle both the multicollinearity and the presence of extreme values in the covariates corresponding to high levels of air contamination. The Huber and Tukey loss functions are considered to obtain robust estimators of the parameters involved in the LMM. We will discuss two data sets which were obtained in different years in the same city.

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