## 5 Conclusions  
In this paper, we have used a path modeling approach to propose causal relationships relating classroom occupancy and outdoor environmental variables with classroom ventilation and air temperature. Sample data from a two-year experimental study of four naturally ventilated classrooms in a Portuguese school were used to validate the path model. Estimates of the magnitude of the causal effects were obtained, and the unexplained model variance was analyzed considering the selected input variables.  
Concerning the path modeling results obtained for the studied classrooms, it can be concluded that:  
* Indoor and outdoor air temperatures are paramount to classroom ventilation, with standardized total path coefficients of approximately 0.55.
* Other significant determinants of classroom ventilation include solar energy, precipitation, and occupancy (as expressed by metabolic CO\({}_{2}\) production rate), with standardized total path coefficients 0.24, \(-\)0.18, and 0.17, respectively.
* The model only explained 58% of the ventilation variance, whereas for the indoor air temperature it explained 75% of the variance. This difference is attributed to the absence of important personal and contextual factors regarded as determinants of occupants' behavior. Regarding to the use of path modeling and SEM more generally to research natural ventilation, it can be concluded that:
* Causal relationships derived from building physics and principles of occupants' behavior resulted in a path model with an excellent fit to the sample covariance data gathered from naturally ventilated classrooms.
* Compared to the commonly used multiple and logistic regression methods, path modeling can expand the understanding of natural ventilation, providing detailed direct, mediation, and feedback effects as well as quantifying the unexplained variance associated with individual model output variables such as the air change rate and indoor air temperature.
* As a collection of statistical procedures that complements path analysis with exploratory factor analysis, SEM is well suited for multi-domain studies; thus, an extension of the present research to include additional personal and contextual determinants of occupants' behavior would allow for further insights.  
Finally, practical advice to improve the studied classrooms' indoor air quality, especially during wintertime, would include raising the awareness of school management, janitors, teachers, and students regarding the importance of appropriate classroom heating and classroom ventilation (i.e., window opening/closing) best practices.  
Conceptualization, R.D.; methodology, R.D.; validation, A.M.R., M.d.G.G. and F.P.; formal analysis, R.D.; investigation, R.D.; resources, R.D. and F.P.; data curation, R.D. and F.P.; writing--original draft preparation, R.D.; writing--review and editing, R.D., A.M.R. and M.d.G.G.; visualization, R.D. and A.M.R.; project administration, M.d.G.G. All authors have read and agreed to the published version of the manuscript. The second and fourth authors acknowledge the Portuguese Foundation for Science and Technology (FCT) for funding the CERIS research unit (UIDB/04625/2020). The data presented in this study are available on request from the corresponding author due to privacy reasons. The authors declare no conflicts of interest.