## 4 Empirical Analysis
### Formation of Analysis Modeling with the SEM-VALTM Model  
The SEM-VALTM model was developed with three latent variables, economic, social, and environmental, incorporating 15 indicators that are stationary and co-integrated at the same level. This model effectively demonstrates the influence of relationships through the SEM-VALTM model. Detailed results are shown in Figure 3.  
From Figure 3, it is evident that the latent variables exhibit both direct and indirect effects. The SEM-VALTM model has been validated with the following criteria: the \(\chi^{2}/\mathrm{df}\) value is 1.55, RMSEA value is 0.01, RMR value is 0.001, GFI value is 0.96, AGFI value is 0.94, R-squared is 0.96, the F-statistic is 225.00 (with a probability of 0.00), the ARCH test is 20.15 (with a probability of 0.1), and the LM test is 1.11 (with a probability of 0.10). Moreover, the SEM-VALTM model has passed the test for Best Linear Unbiased Estimation (BLUE) completely. The analysis reveals that the SEM-VAL model effectively analyzes the relationships and the direction of these relationships between the latent variables: the economic sector and environmental sector show an inverse relationship; the economic sector and social sector show a positive relationship; and the social sector and environmental sector show an inverse relationship. The relationships between the latent variables arise  
Figure 3: Analysis of Causal Relationships in the SEM-VALTM Model. *** denotes a significance, = 0.01, ** denotes a significance, = 0.05.  
from the observed variables in each sector, which exhibit varying levels of influence, as detailed below:  
1. Economic Sector: At a statistical significance level of \(\alpha\) = 0.01, the observed variable with the highest influence is the industrial structure rate \((\Delta\ln(In))\), followed by the per capita GDP rate \((\Delta\ln(Y))\), the foreign tourist rate \((\Delta\ln(Ft))\), the urbanization rate \((\Delta\ln(Utr))\), the indirect foreign investment rate \((\Delta\ln(If))\), the total exports rate \((\Delta\ln(E-m))\), and the government expenditure rate \((\Delta\ln(Ge))\), respectively. 2. Social Sector: At a statistical significance level of \(\alpha\) = 0.01, the observed variable with the highest influence is the consumer protection rate \((\Delta\ln(Sc))\), followed by the social security rate \((\Delta\ln(Se))\), the employment rate \((\Delta\ln(Es))\), and the health and illness rate \((\Delta\ln(Hr))\), respectively. 3. Environmental Sector: At a statistical significance level of \(\alpha\) = 0.01, the observed variable with the highest influence is the total energy consumption rate \((\Delta\ln(Ee))\), followed by the green technology rate \((\Delta\ln(Eg))\), the renewable energy rate \((\Delta\ln(Ei))\), and carbon dioxide emissions \((\Delta\ln(CO_{2}))\), respectively. Thus, the SEM-VAL model effectively demonstrates the detailed relationships among causal factors, including both direct and indirect effects. The magnitude of influence is detailed in Table 3.  
Based on Table 3, the SEM-VALTM model has successfully passed validity checks, with RMSEA and RMR values approaching 0, indicating good model fit. Additionally, the GFI and AGFI values are close to 1, further confirming model adequacy. The examination of BLUE (Best Linear Unbiased Estimation) did not reveal issues of heteroskedasticity, multicollinearity, or autocorrelation. In terms of model performance, the determination coefficient (R-square) is 97%, indicating that the model explains 97% of the variance in the dependent variables, and the F-test value is 75.05, significant at the 1% level, indicating overall model significance. The analysis results show that the economic sector has a direct effect on the social sector of 39% in the same direction at the 1% significance level. This implies that a 1% change in the economic sector leads to a 39% change in the social sector in the same direction. The economic sector has a direct effect on the environmental sector of 71% in the opposite direction at the 1% significance level.