## 1 Introduction
However, an important drawback of PCA is the fact that factors do not often have straightforward interpretation [3]. Other alternative methods to PCA are the positive matrix factorization (PMF) [5], the multilinear engine (ME) [6], and multivariate curve resolution alternating least squares (MCR-ALS) [7], which have been utilized for the analysis of the factors contributing to atmospheric pollution, such as climatic variables (precipitation, air temperature, relative humidity, etc.) or different individual pollutants. Recently, the Rasch model has been proposed as a technique to obtain a measure of atmospheric pollution considering several individual pollutants [8] and it has been also used to consolidate several measures of ozone levels into an overall variable to simplify the interpretation of ambient ozone in a medium-sized urban area [9]. With the formulation of the Rasch model as a measure technique [10], more information can be obtained than using the aforementioned methods. Thus, the influence of each individual pollutant on the environmental deterioration for a particular area, anomalies in any data at every sample location or relationships between different factors is analyzed using a probabilistic approach. The Rasch model have been successfully used in many studies, proven their practical utility in different cases related to the environment [8; 9; 11; 12; 13]. As far as we know, there is no previous application of this useful methodology in this field. The present work is focused on extending and promoting the use of the Rasch model for the investigation and evaluation of atmospheric pollution in different locations, considering not only the main individual pollutants but also meteorological variables which exert an important influence on the contamination of the atmosphere. Some meteorological factors generate increased pollutants concentrations during episodes of high atmospheric stability and low wind speeds because of restricted dispersion [14]. It has been also reported that some pollutants exhibited a significative correlation with some climatic variables, usually positive with temperature [15] and inverse with precipitation [16]. However, other climate factors, as relative humidity and solar radiation, also affect some pollutant levels [2]. Moreover, stable atmospheric conditions increase the importance of urban-derived pollutants for urban air pollution levels, because of the low dispersion [17; 18]. Although a Rasch analysis can also provide detailed evidence of anomalies (through the misfitting analysis) with respect to the operation of any particular variable which may over or under discriminate relative to the summary discrimination of all variables, and anomalies with respect to the statistical independence of the variables, this analysis is not shown. Additional information about this issue can be obtained, for instance, in [PERSON] et al. [9]. The objectives of this study are to: (1) Analyze the use of the Rasch model as a measurement tool to estimate with a rational basis a representative value of the atmospheric pollution in urban and rural sites; (2) utilize the Rasch methodology to find out how each individual pollutant and meteorological variable has an influence on the atmospheric pollution level; and (3) compare the pollution patterns in each location.