# Safety Risk Assessment in Urban Public Space Using Structural Equation Modelling
## 3 Materials and Methods
### Introduction of SEM  
SEM (structural equation modelling) is a multivariate statistical method that includes path analysis and factor analysis. It can analyze the relationship between measurement variables, latent variables, and errors. It can also obtain the impact on dependent variables from the analysis of independent variables. SEM uses AMOS (analysis of moment structures) software to draw and browse the model through the visualization module; it can also fit the data collected through the questionnaire with various indexes of the model, and finally output the best model. When the fit indexes reach the standards, the model is scientific. The indexes include relative-fit indexes and absolute-fit indexes. The main indexes and standards are shown in Table 4.  
SEM can be divided into EFA (exploratory factor analysis) and CFA (confirmatory factor analysis). This paper used CFA to verify the fitting degree of the index system and the questionnaire data and finally to judge whether the index system is established. CFA is a method of measuring whether the relationship between the measured factors and the measured items is consistent with the researcher's predictions. SEM consists of a measurement model (see Equations (1) and (2)) and a structural model (see Equation (3)).  
\[X=\Lambda_{x}\xi+\delta \tag{1}\]  
\[Y=\Lambda_{y}\eta+\varepsilon \tag{2}\]  
Equation (1) defines the relationship between the explicit observation variable \(X\) and the implicit observation variable \(\xi\); Equation (2) defines the relationship between the explicit latent variable \(Y\) and the implicit latent variable \(\eta\). \(\delta\) is the residual of the dominant observed variable \(X\); \(\eta\) is the residual of the dominant latent variable \(Y\); \(\Lambda_{x}\) is the regression coefficient of \(\xi\); \(\Lambda_{y}\) is the regression coefficient of \(\eta\).  
\[\eta=B\eta+\Gamma\xi+\zeta \tag{3}\]  
Equation (3) represents the relationship between the implicit observation variable \(\xi\) and the implicit latent variable \(\eta\). \(B\) is the coefficient matrix between hidden, latent variables; \(\Gamma\) is the coefficient matrix composed of hidden observed variables and hidden latent variables; \(\zeta\) is the residual of the equation.  
The standardized path coefficient obtained according to the CFA model can calculate the weight of each index and then obtain the importance of each index. Equation (4) is as follows:  
\[P_{i}=\frac{t_{i}}{\sum_{i}^{n}t_{i}} \tag{4}\]  
where \(P_{i}\) is the weight coefficient of the index, and \(t_{i}\) is the path coefficient of the index.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline  & **Fit Index** & & **Standard** \\ \hline Relative-fit index & Root mean square error of approximation & RMSE & \textless{}0.05 & Qualified \\  & Goodness of fit & GFI & \textless{}0.9 & Qualified \\ Absolute-fit index & Chi-square degree of freedom ratio & \(\chi^{2}/\text{df}\) & \textless{}3.00 & Qualified \\  & Comparative fit index & CFI & \textgreater{}0.9 & Qualified \\  & Normed fit index & NFI & \textgreater{}0.9 & Qualified \\ \hline \hline \end{tabular}
\end{table}
Table 4: The main indexes and standards [38].