## 3 Results  
### Structural Equation Modeling for Effluent T-N  
#### 3.1.1 Path Model of Effluent T-N  
The initial path model for effluent T-N concentration (Figure 3a) consists of seven variables, including the target: airflow rate (B_Airflow), return-sludge ratio (B_Sludge return ratio), DO concentration in the aeration tank (B_DO), MLSS concentrations in the aeration tank (B_MLSS), ammonia and nitrate concentration in the aeration tank (Oxic_NH4-N and Oxic_NO3-N), and effluent T-N concentration (Effluent T-N). These variable configurations fully explain the theoretical knowledge that nitrate and ammonia in the aeration tank affect effluent T-N. After an initial trial of model setting with minimum variables as Oxic_NH4-N and Oxic_NO3-N, B_DO and Effluent T-N, other variables were added or removed by repetitively checking the fitness to obtain the best model showing acceptable index values. In the confirmed initial path model, the indices showed that its fitness was acceptable except for an RMSEA of 0.089 (Table 3). Figure 3: _Cont._  
The direction of each path and significant results are shown in the initial path model (Figure 3a). The path results of statistical significance showed that the two paths from B_MLSS to both Oxic_NO\({}_{3}\)-N and Oxic_NH\({}_{4}\)-N did not satisfy the 95% level of significance (\(p<0.05\)). Comparing the significant path coefficients except for these paths, there were three paths that had relatively high importance. First, airflow rate (B_Airflow) had a relatively high effect on MLSS concentration in the bioreactor. The second, the strength of the path from the NO\({}_{3}\)-N concentration in the oxic tank (Oxic_NO\({}_{3}\)-N) to the effluent T-N (Effluent T-N) concentration was high, a natural result in theory. Consistent with the theory is the return-sludge ratio (B_Sludge return ratio) having a large influence on the DO (dissolved oxygen) concentration in the bioreactor (B_DO), and B_DO having a significant effect on both NH\({}_{4}\)-N and NO\({}_{3}\)-N concentration in the aeration tank. The strength of the path from Oxic_NO\({}_{3}\)-N to effluent T-N in the aeration tank was high, as its path coefficient was 0.61, and significant (\(p<0.05\)), whereas the path from Oxic_NH\({}_{4}\)-N to effluent T-N was not significant. This result explains the mechanism of nitrogen removal in the activated-sludge process. When nitrification efficiency is high, ammonia concentration in the aeration tank would be low. The standardized path coefficient means the level of influence, and it corresponds to the regression coefficient in the standardized model. In this respect, it is reasonable that the path coefficient from B_Airflow to B_MLSS is high, and the path coefficient to B_DO is low (\(-0.24\)). The DO concentration measured in the reactor indicates the remaining DO after being used for carbon oxidation and nitrification. When the airflow rate is excessive, then it is possible to have a linear correlation with DO concentration. However, the effect of MLSS concentration on nitrate and ammonia nitrogen was evaluated as statistically insignificant. This is due to the fact that  
Figure 3: Developed path model for effluent T–N concentration. (dashed line: insignificant path coefficient, ***: \(p\)-value \(<0.001\)). (**a**) Initial path model; (**b**) modified path model. MLSS concentration is a composite result of microbial growth, the amount of returned sludge and its degree of concentration, and inflow rate. The deduced initial path model was verified with the prepared data group for validation and not used in the model setup. Validation fitness was acceptable, with a Q value of 1.373, GFI of 0.976, AGFI of 0.938, RMSEA of 0.047, and CFI of 0.979 (Table 3). The initial path model for effluent T-N was enhanced to describe the causal relationships of a larger number of variables (Figure 3b). As the initial path model could not explain the effect of influent variation, the measured variables of bioreactor inflow concentrations were added and tested with fitness indices.