## 4 Model Construction and Fit Evaluation  
### Model Construction  
Structural Equation Modeling (SEM) is a quantitative data analysis method that can handle multivariate relationships and account for latent variables. It allows for a detailed examination of complex theoretical causal relationships [38]. In practical research, factors influencing hospitals, such as medical quality and the convenience of transportation facilities, are difficult to observe directly and require a series of observable indicators for indirect measurement. SEM can handle the relationships between latent and observed variables, providing an accurate reflection of the real situation regarding hospital traffic attraction.  
The structural equation model consists of a measurement model and a structural model, as shown in Figure 4. The measurement model analyzes the relationships between observed variables and latent variables, with the expressions given in Equations (4) and (5):  
\[y =A_{y}\eta+\varepsilon \tag{4}\] \[x =A_{x}\xi+\delta \tag{5}\]  
Figure 4: Schematic diagram of the structural equation model.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Latent Variable**} & \multirow{2}{*}{**Observed Variable**} & \multicolumn{2}{c}{**Standardized Factor Loading**} & \multirow{2}{*}{
\begin{tabular}{c} **Standardized Factor Loading** \\ **(Specialized Hospital)** \\ \end{tabular} } \\  & & **Factor Loading** & & **Standardized Factor Loading** \\  & & **(General Hospital)** & & **(Specialized Hospital)** \\ \hline \multirow{4}{*}{hospital size} & construction area & 0.630 & 0.813 \\  & number of beds & 0.829 & 0.901 \\  & number of medical departments & 0.750 & 0.695 \\ \multirow{2}{*}{medical level} & number of national key specialties & 0.907 & 0.881 \\  & number of positive comments after diagnosis & 0.899 & 0.761 \\ \multirow{2}{*}{traffic accessibility} & number of bus routes & 0.722 & 0.878 \\  & number of parking spaces & 0.870 & 0.782 \\ \multirow{2}{*}{traffic attraction} & average daily outpatient volume & 0.617 & 0.798 \\  & average daily inpatient volume & 0.908 & 0.830 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Rotated component matrix of latent variables.  
In the equations, \(y\) represents the vector of endogenous observable variables within the hospital; \(A_{y}\) represents the factor loading matrix of \(y\) on \(\eta\); \(\varepsilon\) represents the error term for the endogenous observable variables; \(x\) represents a vector composed of the hospital's exogenous manifest variables (including factors such as construction area, number of beds, and number of medical departments, etc.); \(A_{x}\) represents the factor loading matrix of \(x\) on \(\xi\); and \(\delta\) represents the error term for the exogenous observable variables.  
The structural model is used to explain the causal relationships between latent variables, and the expression is given in Equation (6):  
\[\eta=B\eta+\Gamma g+\zeta \tag{6}\]  
In the equation, \(\eta\) represents the vector of endogenous latent variables of the hospital; \(B\) denotes the coefficient matrix reflecting the interrelations among endogenous latent variables; \(\xi\) refers to the exogenous latent variables of the hospital (including hospital size, medical level, and traffic accessibility); and \(\zeta\) represents the residuals that are difficult to predict or explain within the model.