## 3 Results and Discussions
### Analysis of the Rasch Measure: Atmospheric Pollution  
One of the main outputs of the Rasch model is the denominated variable map. In this particular case, all pollutants and climatic variables and days are displayed in the same scale (Figure 3). In consequence, the relative distribution of the days is provided in the upper half of the continuum, according to the associated atmospheric pollution, which has been achieved by means of the 13 pollutants and climatic variables taken into account, and, similarly, these items are provided in the lower half of the diagram, classified according to the influence on atmospheric pollution. The item that obtained the highest measure in all three studied locations, and is to the right in the continuum (Figure 3), is the CO (their measures were 3.88, 2.57, and 2.65, in Badajoz, Caceres and Monfrague, respectively; see Table 4). This means it is the less common item, i.e., its influence on atmospheric pollution is the lowest. The same is apparent in Table 4 because its raw score is consequently the lowest. At the other extreme, the lack of precipitation (it is represented as rainfall in Figure 3, Tables 4 and 5) is situated (their measures were \(-\)3.88, \(-\)3.27, and \(-\)3.72, in Badajoz, Caceres and Monfrague, respectively; see Table 4), with the highest score, being the more common item because \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Category** & **Observed Count (\%)** & **Observed Average** & **Sample Expected** & **Infit MNSQ** & **Outfit MNSQ** & **Structure Calibration** \\ \hline \multicolumn{8}{c}{**Badajoz**} \\ \hline
1 & 41 & \(-\)1.97 & \(-\)2.00 & 1.11 & 1.06 & None \\
2 & 20 & \(-\)0.82 & \(-\)0.73 & 0.74 & 0.93 & \(-\)0.47 \\
3 & 14 & \(-\)0.30 & 0.28 & 1.04 & 1.14 & \(-\)0.16 \\
4 & 10 & 0.20 & 0.16 & 0.71 & 0.63 & 0.25 \\
5 & 15 & 1.68 & 1.66 & 1.08 & 1.76 & 0.39 \\ \hline \multicolumn{8}{c}{**Caceres**} \\ \hline
1 & 43 & \(-\)1.66 & \(-\)1.64 & 0.96 & 0.98 & None \\
2 & 22 & \(-\)0.66 & \(-\)0.71 & 0.80 & 0.65 & \(-\)0.47 \\
3 & 12 & \(-\)0.25 & \(-\)0.26 & 0.95 & 1.29 & 0.16 \\
4 & 8 & 0.09 & 0.15 & 0.86 & 0.88 & 0.39 \\
5 & 15 & 1.30 & 1.30 & 1.11 & 2.19 & 0.48 \\ \hline \multicolumn{8}{c}{**Monfrague**} \\ \hline
1 & 45 & \(-\)2.52 & \(-\)2.53 & 1.01 & 1.03 & None \\
2 & 19 & \(-\)0.88 & \(-\)0.89 & 1.00 & 0.97 & \(-\)0.83 \\
3 & 11 & \(-\)0.23 & \(-\)0.09 & 0.99 & 1.14 & 0.10 \\
4 & 9 & 0.45 & 0.45 & 0.73 & 0.94 & 0.31 \\
5 & 16 & 1.52 & 1.48 & 1.01 & 1.46 & 0.41 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Response scale use: number of times the category was selected considering all days and items, pollutants and climatic factors (observed count), mean value of logit positions modelled in the category (observed average), optimum values of the average logit positions for the data (sample expected), and logit calibrated difficulty of the step representing the transition points between one category and the next (structure calibration). Infit and outfit MNSQ are mean-square fit statistics to verify if items fit the model. this climatic variable affects all days, i.e., it is the most influential item on the atmospheric pollution in all locations. After analyzing the variable maps (Figure 3) and the distribution of all items, important differences are apparent between the urban sites and the rural one. As it could be expected, because it is a National Park, Monfrague is not affected by many individual pollutants. Only ozone has an important impact at this location, and SO\({}_{2}\) has a minor influence (probably generated from processes of organic decomposition, although the concentrations were always very low). With respect to the climatic variables, besides the lack of precipitation (which is the most influential factor on atmospheric pollution as it was previously indicated), the other four factors are important during many days, and they are close to tropospheric ozone, indicating their influence on this pollutant. Figure 3: Variable maps for the three locations.