## Materials and Methods
### Structural Equation Model  
#### 2.2.1 Path Model  
Path analysis is an extension of multiple regression analysis [34], with a path model that depicts the direct and indirect effects of independent variables on one or more independent variables based on a hypothesis to be verified. Verification of the path model is performed by assigning data to the model and determining fitness. There are four types of direct causal relationships shown in Figure 1. Path analysis is the basis for constructing the basic structure of the SEM. Through path analysis, the causal relationship can be represented in more detail by confirming the inherent causal effects as  
\begin{table}
\begin{tabular}{c c} \hline
**Items** & **Variables** \\ \hline Weather conditions & Air temperature (\({}^{\circ}\)C), rainfall (mm), relative humidity (\%) \\ \hline Primary settling tank * & Water temperature (\({}^{\circ}\)C), pH, BOD (mg/L), COD (mg/L), SS (mg/L), \\  & T–N (mg/L), T-P (mg/L), alkalinity, S-BOD, HRT (h) \\ \hline  & Flow (m\({}^{3}\)/d), water temperature (\({}^{\circ}\)C), pH, DO (mg/L), MLSS (mg/L), MLVSS (mg/L), SVI, \\  & sludge return ratio (m\({}^{3}\)/d), \\  & Sludge return ratio (\%), F/M ratio, BOD loading (kg/m\({}^{3}\)-day), SRT (day), \\ Bioreactor ** & A-SRT (day), Internal sludge-return ratio (\%), ORP (mV), \\  & PO\({}_{\text{d}}\)-P (mg/L, at both anaerobic and anoxic tanks), \\  & NH\({}_{\text{d}}\)-N (mg/L, at both anoxic and uric tanks), \\  & NO\({}_{\text{S}}\)-N (mg/L, at both anoxic and uric tanks), \\  & air flow (m\({}^{3}\)/day), reactor volume (m\({}^{3}\)), HRT (h) \\ \hline  & Water temperature (\({}^{\circ}\)C), pH, BOD (mg/L), COD (mg/L), SS (mg/L), T–N (mg/L), T-P \\  & (mg/L), alkalinity, HRT (h) \\ \hline \end{tabular}  
*: The items will be expressed with indication of “B\(\_\)in” (ex: B\(\_\)in\(\_\)BOD). **: The items will be expressed with indication of “B\(\_\)” (ex: B\(\_\)SRT).  
\end{table}
Table 1: Collected data variables.  
the direct, indirect, and total effect. The hypothesized relationship, illustrated at each path, is tested on its acceptance or not by the path direction and the significance of the path coefficient. The standardized path coefficient is key to explaining the strength of the causal path, which enables to compare it with other coefficients in one model. The reliability of the path coefficients should be confirmed based on test statistics such as critical ratio (C.R.) value and p-value. If the C.R. is above 1.96 and the p-value is smaller than 0.05, then the path is reliable. In this research, the p-value was used to judge reliability.  
To set up the path model for effluent T-N and T-P concentrations, the minimum variables considered to theoretically affect the targets were used to comprise the initial path models, respectively. Then, the initial model was examined for fitness using the fitness indices suggested in Table 2. Then, If the initial path model was judged to be appropriate, the model was extended by adding the variables and determining the fitness again. Through repetition of this process, the modified path model was derived. This method of establishing the initial model and then confirming the modified final path model through expansion and validation is a generalized process to deduce the rational model, which also has been proposed by [PERSON] et al. (2015) [PERSON] et al. (2015).