## 3 Materials and Methods
### Method
#### 3.2.3 Gravity Model Building  
The gravity model is one of the widely used methods to study the tourists travel from one place to another, which belongs to the family of spatial interaction models. Its significant advantages rely on its simply used and good ability to produce accurate results, which are easily explained by the spatial relationship and demonstrate the relationship between two entities considering their different characteristics.  
The gravity model assumes the trade flow (tourist flow can be regarded as a type of trade flow) transferring from the origin to destination is positively affected by the reciprocal of the distance between the two and positively affected by the characteristics of the two regions (e.g., population, income, GDP) [72; 73]. In addition, these concepts allow for different interpretations. For instance, spatial separation, which is always regarded as physical distance, can be expressed by political or cultural distance. Just as [PERSON] said, the traditional gravity model also needs to consider more variables to statistically show the potential relationship and provide more theoretical and practical implications [74]. Thus, this research takes the gravity model as the basic statistic theory to analyze the effects of tourism network structure on tourism performance.  
Here, the tourist flow from one country is shown as the dependent variable in this study, representing the international performance; meanwhile, the node's characteristics can be seen as the influencing characteristics, and the global measurements of the GTN's structure are shown as mediator variables in the equation as follows:  
\[ITA_{ijt}=\frac{C_{it}{}^{\beta_{1t}}C_{jl}{}^{\beta_{2t}}}{d_{ij}{}^{\beta_{3} }}\cdot E_{jt} \tag{1}\]  
where \(ITA_{ijt}\) represents the tourist flow from \(i\) to \(j\) in the year of \(t\), and \(d_{ij}\) is the spatial distance between the two, which can be calculated from the latitude and longitude of each region' s geographical center and then transformed into a geodetic coordinate system; \(C_{it}\) and \(C_{jl}\) represent the measurement of the node \(i\) and \(j\) in the year of \(t\), respectively; and \(E_{ij}\) is a normal distributed error.  
The gravity model can be converted as a linear model to estimate all these factors' impacts. This research applies the mixed-effect multi-level regression model considering different countries' features. The mixed-effect model is developed to account for both network and temporal dependencies [75]. The results provide means and regression estimates of the factors affecting global tourism networks as well as evidence of statistical dependencies [5]. The mixed-effect regression model from the gravity model conversation is displayed as Equation (2), and it is calculated based on the mixed-effect modular of software State v16.0.  
\[\begin{array}{ll}\ln ITA_{ijt}&=&\beta_{1t}\ln DC_{it}\ +\ \beta_{2t}\ln DC_{it}\\ &+\ \beta_{3t}\ln CC_{it}\ +\ \beta_{4t}\ln CC_{it}\ +\ \beta_{5t}\ln BC_{it}\ +\ \beta_{6t}\ln BC_{it}\ +\ \beta_{7t}\ln EC_{it}\ +\ \beta_{8t}\ln EC_{it}\\ &+\ \beta_{9t}\ln LCLC_{it}\ +\ \beta_{10t}\ln LCLC_{it}\ +\ \beta_{11t}Indis_{ij}\ +\ s_{it}\ +\ t_{it}\ +\ \epsilon_{ijt}\\ \end{array} \tag{2}\]  
where \(\beta_{1t}\) to \(\beta_{11t}\) represent the coefficients of all the variables we selected in the year of \(t\); \(s_{it}\) shows the effect of the source country \(i\); \(t_{it}\) is the effect of target country \(j\); and \(\epsilon_{ij}\) is a residual error in regression model.  
For an objective estimation, this research firstly arranges the model as longitudinal panel data to obtain the effects of all the variables overhaul; then, it calculates the coefficients between 222 regions for each year from 1995 to 2019, which can help to understand the changes of GNT. Additionally, owing to the possible multicollinearity among variables, before calculating the coefficients, the multicollinearity test must be conducted first.