Open Conference Systems, 50th Scientific meeting of the Italian Statistical Society

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Modelling the effect of Traffic and Meteorology on Air Pollution with Finite Mixtures of M-quantile Regression Models
Simone Del Sarto, Maria Francesca Marino, Maria Giovanna Ranalli, Nicola Salvati

Last modified: 2018-05-28


Between 2012 and 2015, the PMetro project collected space-time meteorological, aerosol and gas measurements by using dedicated instruments integrated on one of the cabins of the Minimetro, a public conveyance of the town of Perugia. PMetro data allow us to investigate real time tropospheric dynamics in urban contexts. In this work, the effect of vehicular traffic and meteorological measurements on the distribution of particulate matter (PM) has been studied by fitting a Finite Mixture of M-quantile regression models. The proposed methodology accounts for heterogeneity in the data using random effects with a discrete distribution estimated directly from the data; this is useful to handle departures from normality of the distribution of the random effects. In addition, it allows to investigate the relationship between air pollutants and the covariates at different M-quantiles of the conditional distribution of PM. The results show that radon concentration and vehicular traffic have the largest effect on the distribution of PM. In particular, the parameter estimate for radon concentration is always positive and increases along the M-quantiles, while the effect of vehicular traffic is the same both for lower and higher PM concentrations. These results can also be used to provide guidelines for policy makers.

Abstract in italiano. Fra il 2012 ed il 2015, il progetto PMetro ha raccolto dati meteo e sulla concentrazione di particolato atmosferico e gas usando strumentazione appositamente installata su una delle cabine del Minimetro, una linea di trasporto urbana su rotaia della città di Perugia. In questo lavoro usiamo modelli M-quantile a mistura finita per studiare l’effetto del traffico e delle variabili meteo sulla distribuzione del particolato atmosferico. I risultati principali mostrano che la concentrazione di radon ed il traffico sono le variabili che incidono maggiormente, con andamenti, tuttavia, diversi per diversi valori degli M-quantili.


1. Aitkin, M.: A general maximum likelihood analysis of overdispersion in generalized linear models. Statistics and Computing 6, 251–262 (1996)

2. Aitkin, M.: A general maximum likelihood analysis of variance components in generalized linear models. Biometrics 55, 117–128 (1999)

3. Alfò, M., Salvati, N., Ranalli, M.G.: Finite mixtures of quantile and M-quantile regression models. Statistics and Computing 27(2), 547–570 (2017)

4. Bianchi, A., Fabrizi, E., Salvati, N., Tzavidis, N.: M-quantile regression: diagnostics and parametric representation of the model. Working paper (2015). Available at

5. Castellini, S., Moroni, B., Cappelletti, D.: PMetro: Measurement of urban aerosols on a mobile platform. Measurement 49, 99–106 (2014)

6. Dempster, A., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society. Series B (Methodological) 39, 1–38 (1977)

7. Geraci, M., Bottai, M.: Linear quantile mixed models. Statistics and Computing 24, 461–479 (2014)

8. Kneib, T.: Beyond mean regression. Statistical Modelling 13(4), 275–303 (2013)

9. Laird, N.M., Ware, J.H.: Random-effects models for longitudinal data. Biometrics 38(4), 963–974 (1982)

10. Pöschl, U.: Atmospheric aerosols: composition, transformation, climate and health effects. Angewandte Chemie International Edition 44(46), 7520–7540 (2005)

11. Seinfeld, J.H., Pandis, S.N.: Atmospheric chemistry and physics: from air pollution to climate change. John Wiley & Sons (2012)


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