## 4 Results and Discussion  
### Validation of the Model Structure  
The path model in Figure 5 with the assumptions/constraints presented in Table 1 and covariance sample data from Table 3 converged to an admissible solution with chi-square close to one, which is statistically significant at the 0.05 level (\(\chi^{2}(5)=0.790\) with \(p=0.978\)); hence, the exact fit hypothesis is not rejected. The relative fit of the model is a significant improvement over the baseline model fit with CFI = 1.00 (\(>\)0.95); according to the result of GFI = 1.00 (\(>\)0.95), the covariance matrix predicted by the model completely explains the variability in the sample covariance matrix. The RMSEA value of the model is 0.000 (\(<\)0.05 with 90% confidence interval 0.000-0.000) and the close fit hypothesis is not rejected (\(p=1.000\)). The highest coefficient of the standardized residual covariance matrix is 0.651 (\(<\)2.00) and the model's SRMR is 0.00 (\(<\)0.08). The Akaike Information Criterion (AIC) is 33,997. Table 4 presents the unstandardized estimates (Unst. ), corresponding standard errors (S.E. ), and standardized estimates (St.) of the \"full\" path model parameters. The variances and covariances of the model variables (\(x\) and \(y\)) are equal to those determined from the standard deviations and correlation coefficients in Table 3.  
In addition to the magnitude of the path coefficients, their statistical significance is also important. Several of the presented paths are not significant, such as the effects of wind speed (\(\overline{\text{WS}}\)) and relative humidity (\(\overline{\text{RH}}\)) on ventilation. The covariances between wind speed and relative humidity or solar radiation are also non-significant (not shown, but in accordance with Table 3). The covariance \(\psi_{12}\) between the residues of the output model variables is the least significant. After removing the statistically non-significant covariance \(\psi_{12}\) and trimming the resulting path coefficients to leave only those that were statistically significant to the \(p<0.01\) level, the \"trimmed\" path model was obtained, with unstandardized and standardized parameter estimates presented in the rightmost columns of Table 4.  
For the trimmed-model, the chi-square statistic is \(\chi^{2}(6)=0.783\) (\(p=0.993\)) and other fit statistics are CFI = 1.000, GFI = 1.000, RMSEA = 0.000 (0.000-0.000, \(p=1.000\)), SRMR = 0.000, and AIC = 30,619. Except for the lower AIC, no significant difference is found between the goodness of fit statistics of the trimmed and full path models; moreover, both models have similar path coefficients. These results confirm the validity of the internal structure proposed in Figure 5. As discussed in Section 3.2, both building physics and occupants' adaptive behavior principles apply to the study of ventilation when using the path model approach, and should also apply to the case of structural equation modeling more generally. This is an important conclusion when considering that structural equation modeling allows for the simultaneous use of observable variables (included in this study) and unobservable constructs (not included) characterizing students' and teachers' group and personal attributes.