## 3 Results and Discussions  
### Data Response to the Model at Each Site  
After processing the matrix of categorical values by the WINSTEPS program, the first information to be considered is if the data fit the model reasonably by analyzing the infit and outfit statistics. Consequently, according to the infit and outfit MNSQ values contained in Table 1 (between 1.09 and 1.23), there is a clear evidence about the agreement between the data and the model. Moreover, the mean standardized (ZSTD) infit and outfit, which are the sum of squares standardized residuals given as a Z-statistics [21], are expected to be 0; in this case study, they both are near zero for samples (days) at the three locations (Table 2). However, when items are considered, better results are obtained for Monfrague, with values near zero, than for Badajoz or Caceres (Table 1), denoting that the data fit the model better in the rural site than in the urban locations, despite in all cases the overall fit is acceptable. The same is apparent when the standard deviation of the infit MNSQ is analyzed for days. This is also an index of the overall misfit and a value below 2 is considered acceptable [22]. There are no important misfits in this case study because their values are 0.63, 0.74, and 0.81 (Table 2), also indicating an acceptable overall fit of the data. Figure 2: Schematic diagram of the stages involved in the formulation of the Rasch model. The next step is to analyze the internal consistency of data, in the sense that expected results with the Rasch model will be accurate if measures of the items are properly performed, without significant errors. Thus, there is a reliability statistics, which is expected to be close to 1. Acceptable values would be over 0.7 ([PERSON], 2018). In this study, reliability of days was 0.66 for Badajoz and Monfrague, and 0.61 for Caceres; for pollutants and climatic factors, they were 0.99 for all locations. In spite of computing \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **Total Score** & **Count** & **Measure** & **Model Error** & \multicolumn{3}{c}{**Infit**} & \multicolumn{3}{c}{**Outfit**} \\ \cline{5-10}  & & & **Badajoz** & & **MNSQ** & **ZSTD** & **MNSQ** & **ZSTD** \\ \hline Mean & 788.4 & 332 & 0.00 & 0.10 & 1.23 & \(-\)1.4 & 1.09 & \(-\)1.4 \\ Standard Deviation & 336.1 & 0 & 1.70 & 0.10 & 0.78 & 5.6 & 0.62 & 5.1 \\ Maximum & 1633.0 & 332 & 3.88 & 0.41 & 2.93 & 9.9 & 2.84 & 9.9 \\ Minimum & 338.0 & 332 & \(-\)3.88 & 0.05 & 0.47 & \(-\)9.9 & 0.49 & \(-\)9.3 \\ \hline \multicolumn{10}{c}{Cáceres} \\ \hline Mean & 699.1 & 304 & 0.00 & 0.08 & 1.23 & \(-\)1.1 & 1.20 & \(-\)0.9 \\ Standard Deviation & 305.3 & 0 & 1.36 & 0.05 & 0.79 & 5.3 & 0.87 & 4.7 \\ Maximum & 1488.0 & 304 & 2.57 & 0.22 & 3.15 & 9.9 & 3.79 & 9.9 \\ Minimum & 325.0 & 304 & \(-\)3.27 & 0.05 & 0.46 & \(-\)8.7 & 0.50 & \(-\)7.9 \\ \hline \multicolumn{10}{c}{Monfragüe} \\ \hline Mean & 772.8 & 333 & 0.00 & 0.10 & 1.16 & \(-\)0.2 & 1.09 & \(-\)0.3 \\ Standard Deviation & 380.8 & 0 & 1.81 & 0.06 & 0.48 & 5.4 & 0.48 & 5.2 \\ Maximum & 1619.0 & 333 & 2.65 & 0.22 & 1.91 & 9.9 & 1.98 & 9.9 \\ Minimum & 355.0 & 333 & \(-\)3.72 & 0.05 & 0.53 & \(-\)8.6 & 0.54 & \(-\)8.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Overall model fit information; summary of all 13 individual pollutants and climatic variables (items) for the three locations: sum of points of the common scale (total score), days or items taken into account (count), logit position of the days and items along the straight line that represents the latent variable, atmospheric pollution (measure), and standard error of measurement (model error). Infit and outfit MNSQ are mean-square fit statistics to verify if items fit the model; infit and outfit ZSTD are standardized fit statistics to verify if items fit the model.