## 4 Discussion
However, due to the characteristic of this study, the implementation of nonlinearity through latent variables, the ideal model transformation process has not been realized. Since the derived path model reflects the nutrient removal mechanism, the attempt of the path model is not meaningless. However, it can be said that the structural equation modeling is more suitable to express causality of wastewater treatment plant data with high measurement uncertainty and complex cause-effect relationships. In addition, it is noteworthy that theoretically known knowledge is somewhat reflected in the SEM proposed in this study. So far, SEM has been mainly used to verify an explored, so there is no case of applying it to the removal mechanism of the sewage-treatment process. This is because the type of process and its mechanism have reliably been recognized for certainty. However, the purpose of this study was to ascertain whether such mechanisms are inherent to the data, and how their causality is expressed with some degree of linearity. As a result, there are not many variables that are linear causative factors of effluent quality. The most obvious factor of linearity was the path from the concentration of nutrients in the aeration tank, the last compartment of the bioreactor, to effluent quality. The complex and linear causal paths between the variables, on the other hand, were found to be rare, but the SEM was constructed to sufficiently reflect the causal relationship between the potential variables. A further consideration in future studies is that more data should be collected. The water quality items used in this research were limited. If the water quality data obtained from the field included various carbon source concentration in the influent, the path model and the developed SEM would have been able to express more mechanisms. The data used in this research included only BOD and COD for carbonaceous material. Therefore, the detailed mechanism could not be implemented in the developed models. In addition, because the T-N removal and T-P removal mechanisms are closely related, modeling of the combination of these two dependent variables could be possible. As already theoretically known, T-N and T-P cannot be removed without a carbon source. The nitrate produced in the oxic tank flows into the anaerobic tank through the settling tank and works as an electron acceptor for anoxic carbon oxidation inhibiting phosphorus release. For this reason, in the developed SEM for T-N, Anaero_PO\({}_{4}\)-P, a variable indicating the phosphorus release is described to be affected by two latent variables such as \"Inflow factor\" and \"React factor\" comprising F/M ratio. In addition, the SEM described the combined effect of the latent variable \"Operational factor\" including aeration flow and the \"Reactor factor\" including F/M ratio to the PO\({}_{4}\)-P concentration in the oxic tank. This reflects that there is an indirect combined effect of the amount of the carbon source and the aeration flow in the oxic tank to the PO\({}_{4}\)-P concentration in the oxic tank. In addition, if excessive aeration is given to the oxic tank to obtain maximum nitrification, oxygen will flow into the anoxic tank by the nitrate return flow, thereby inhibiting denitrification. Therefore, it is hard to simply conclude the relationships between nitrogen and DO as proportional or inverse, as shown in Figure 3. There is an inverse proportional relationship between B_DO and Oxic_NH\({}_{4}\)-N whereas weak positive correlation with oxic_NO\({}_{3}\)-N. This is expressed at the SEM for T-N as that the latent variable \"Operational factor\" has a direct effect to the effluent T-N with high correlation factor, 0.67. For the case of Oxic_NO\({}_{3}\)-N, the fact that it is affected by the latent variable \"Return flow related factor\" with the high correlation value 0.83 can be regarded as reflecting the theoretical fact for the level of Oxic_NO\({}_{3}\)-N decided by the nitrate return ratio.