## 3 Research Methodology
### Research Method
The measurement model describes the latent variables through the corresponding observed variables. \[x =\Lambda_{x}\xi+\varepsilon \tag{1}\] \[y =\Lambda_{y}\eta+\varepsilon \tag{2}\]  
where \(x\) and \(y\) are the vectors of observed variables of exogenous latent variables and endogenous latent variables, respectively; \(\Lambda_{x}\) is the factor loading matrix of \(\xi\) to \(x\); \(\Lambda_{y}\) is the factor loading matrix of \(\eta\) to \(y\); \(\xi\) and \(\eta\) are the vector composed of exogenous latent variables and endogenous latent variables, respectively; \(\varepsilon\) is the vector of observation error. The structural model utilizes exogenous latent variables to elucidate the endogenous latent variables. \[\eta=\text{B}\eta+\Gamma\xi+\zeta \tag{3}\]  
where B is the structural coefficient matrix of endogenous latent variables; \(\xi\) is exogenous, the structural coefficient matrix of latent variables; \(\zeta\) is the residual vector of the model. In this paper, four aspects of terrain spatial perception are proposed. When analyzing the moderating effect of terrain spatial perception on the influence of other factors on P&R use behavior, if the interaction terms are directly constructed for modeling and analysis, the model structure will be very redundant and the correlation between variables will increase, ultimately leading to deviations in the model results [42]. In a confirmatory factor model with multiple factors, if the lower-order factors are closely related and can collectively represent a broader concept in theory, then these lower-order factors can be considered as new measurement indicators to estimate the higher-order factor structure. Therefore, before constructing the SEM-Logit model, a second-order confirmatory factor analysis is used to reduce the dimensionality of the four subjective perception variables, resulting in the extraction of a terrain spatial perception factor. The four subjective perception variables  
Figure 2: Theoretical model. are normalized to the load coefficient of the terrain spatial perception factor. The calculation formula is shown in Equation (4):  
\[\lambda_{r}=\frac{\lambda_{r}}{\sum\limits_{r=1}^{4}\lambda_{r}},r=1,2,3,4. \tag{4}\]  
where \(\lambda_{r}\) is the confirmatory factor model coefficient of the latent variable \(r\). This coefficient is then used as the weight for each factor to calculate the corresponding observation value of the terrain spatial perception. The calculation formula is shown in Equation (5):  
\[TSP=\lambda_{1}SEC+\lambda_{2}CON+\lambda_{3}COM+\lambda_{4}ACC \tag{5}\]  
The utility \(U_{in}\) of motorist \(n\)'s choice of mode \(i\) can be expressed by Equation (6):  
\[U_{in}=V_{in}+\varepsilon_{in}=\beta x_{in}+\varepsilon_{in} \tag{6}\]  
where \(V_{in}\) is the observable utility part, that is, the definite term; \(\varepsilon_{in}\) is the unobservable portion of utility. \(x_{in}\) is the characteristic variable when motorist \(n\) chooses scheme \(i\). \(\beta\) is the parameter to be estimated for the characteristic variable. According to the theory of utility maximization, when a motorist commutes, he will choose the commuting mode with the greatest utility according to his own situation and various factors. Suppose that the set of all travel mode selection schemes that the motorist can choose is \(A\), where the utility of the scheme \(j\) is \(U_{jn}\), then the conditions for the motorist to choose the scheme are:  
\[U_{in}>U_{jn},\;i\
eq j,\;j\in A \tag{7}\]  
According to the research object in this paper, it is defined that the travel mode selection set of motorists consists of only 1 (using P&R) and 0 (driving all the way), so the binary Logit model is adopted for analysis. The probability that the motorist chooses to commute using P&R and driving all the way can be expressed by Equation (8):  
\[P_{in}=\frac{\exp(V_{in})}{\exp(V_{1n}+V_{0n})},\;i=0,1. \tag{8}\]  
where \(V_{in}\) is the utility fixed term of commuting scheme \(i\) selected by car motorist \(n\).