## 4 Results and Discussion
### Estimates of Model Coefficients \(\gamma\) and \(\beta\)  
The previous path analysis provides us with estimated magnitudes of the effects of the observable variables (see Table 4). Figure 6 provides a graphical interpretation of the trimmed model's standardized estimates for the direct effects \(\gamma\) and mediation effects \(\beta\). Starting with the path analysis of \(\beta\) between ventilation and the indoor thermal environment, it can be concluded that both are statistically significant and that their coefficients have opposite signs, confirming the negative feedback loop discussed in Section 3.2. From the magnitude of the standardized estimates, it can be concluded that the reciprocal causal effect is stronger in the direction from thermal environment to ventilation (0.637); in fact, the mediating effect of the indoor thermal environment \(\beta_{12}\) is the best determinant of classroom ventilation, and is much better than the direct effects \(\gamma_{1j}\) from classroom occupancy and outdoor physical variables. Because ventilation is determined by occupants' behavior and is a function of the perceived environment, this result confirms indoor air temperature as the most important determinant of occupants' behavior. However, the proposed path model structure defines the coefficient \(\beta_{12}\) as a mediating effect, with indoor air temperature determined in turn by classroom occupancy and outdoor physical variables. Figure 6b shows that the outdoor air temperature has the largest effect by far on the indoor air temperature, with a standardized path coefficient of 0.939, i.e., one standard deviation change in the outdoor air temperature determines a 0.939 standard deviation change in the same direction in the indoor air temperature. Indeed, previous research is unanimous regarding the effect of indoor and outdoor air temperature on natural ventilation with window airing, concluding that both are very important drivers [34; 78]. The internal structure used in this paper, with the indoor air temperature mediating the outdoor air temperature, allows for the use and association of both these variables in a single model, thereby circumventing the discussion of which temperature should be used [26; 28; 57; 78]. In this approach, occupants perceive the direct effect of the indoor air temperature while retaining the indirect effect of the outdoor air temperature [43]; see Section 4.4.2 for a detailed description of the indirect effects. To analyze the magnitude of the standardized effects \(\gamma_{1j}\) of occupancy and outdoor variables on ventilation, Figure 6a shows that the best predictors of ventilation are precipitation, metabolic CO\({}_{2}\) production rate (occupancy), and solar energy, with standardized coefficients \(-0.204\), \(0.154\), and \(0.153\), respectively. The negative sign for precipitation (also described in [83]) suggests a link between precipitation and window closing, and in turn with a reduction in the air change rate. The results for solar energy show that ventilation increases with increasing solar energy. Because solar energy contributes to the indoor thermal and visual environments, influencing opening/closing of both windows and blinds, these results testify to this combined effect. Regarding classroom occupancy, the statistical significance of the direct effect on ventilation supports larger air change rates for larger class attendance levels, or for classes with older students considering similar attendance. It is interesting to point out the disproportion between the standardized coefficient relating occupancy and ventilation (0.154) as well as in the one relating occupancy and indoor air temperature (0.050).