## Materials and Methods
### Data Collection and Treatment  
Extremadura has six atmospheric pollution monitoring stations (five in medium and small-sized urban sites and one in a rural location), operated by the Department of Environment of the Extremadura Government, which are continuously measuring some air pollutants and meteorological variables ([[http://xtr.gobex.es/repica/index.html](http://xtr.gobex.es/repica/index.html)]([http://xtr.gobex.es/repica/index.html](http://xtr.gobex.es/repica/index.html))), providing measurements every minute. The procedures are established by Spanish legislation (Real Decreto 1073/2002). Pollutants measurements were saved in hourly period and data were collected from 1 January to 31 December 2016. Eight pollutants (NO\({}_{\mathsf{X}}\), NO, NO\({}_{\mathsf{2}}\), O\({}_{\mathsf{3}}\), SO\({}_{\mathsf{2}}\), PM\({}_{\mathsf{10}}\), CO, and benzene) and five climatic variables (precipitation, relative humidity, solar radiation, mean air temperature, and barometric pressure) were considered. Their mean daily value was computed and they were incorporated in a database. In consequence, the final data set is a matrix with 13 columns and 365 rows.  
Next, it was necessary to obtain a measurement of the atmospheric pollution using different individual pollutants and climatic factors, with different units. This important problem may be solved with the application of a measured technique based on the Rasch model [19], using the WINSTEPS v. 3.69 computer program [20]. To do that, first, a transformation of the pollutants and the climatic factor measures to common categories was performed and data were incorporated in the cells of the matrix. Five categories or levels were established; in consequence, measures were categorically coded according to a plan where each pollutant and climatic variable was rated on a scale (1-5) for each day. The minimum and maximum values of the scale were assigned to the maximum and minimum values of each pollutant and climatic factor and other intermediate values for all different days were obtained through interpolation Thus, a measure assigned to level 1 indicates the lowest contribution to atmospheric pollution and, on the contrary, a measure assigned to level 5 indicates the highest contribution to atmospheric pollution. With 13 pollutants and climatic factors taken into account, the highest possible raw score for the days in 2016 is 65 (the most potentially polluted) and the lowest possible score is 13 (the least potentially polluted). Considering all days, the highest possible raw score for pollutants and climatic factors is 1825 (the most influential on atmospheric pollution) and the lowest possible score is 365 (the least influential on atmospheric pollution).  
With respect to the data distribution, the Rasch model has certain distinctive and interrelated features [10]: it is concerned principally with the measurement of individuals (considered days in this study), rather than with distributions among populations, and it is concerned with establishing a basis for meeting a priori requirements for measurement and, consequently, do not invoke any assumptions about the distribution of levels of a trait in a population.  
The main outputs of the program are explained in this work; the empirical hierarchy of the pollutants and climatic factors, which is illustrated using variable maps and related to all days, with each reported in logits, the statistics to show how well the data fit the model, and, moreover, the way to study the unexpected values.