## 3 Materials and Methods
### Robustness Tests  
(1) Replacing the core independent variable. The core independent variable of the policy structure was composed of service, financial, technical, subsidy, and supervision policies. Factor analysis was carried out to reduce the dimensionality of these five indicator variables, and a new policy structure variable was constructed as the core independent variable [44; 46]. The KMO test value was 0.777, the approximate chi-square value of [PERSON]'s sphericity test was 2114.822, and the \(p\)-value was 0.0000, indicating that policy structure indicator data were suitable for factor analysis. Similarly, the evaluation variables of policy implementation were also dimensionally reduced via factor analysis. The KMO test value was 0.809, the approximate chi-square value of [PERSON]'s sphericity test was 2046.309, and the \(p\)-value was 0.0000, indicating that the data of policy implementation evaluation indicators were suitable for factor analysis. The benchmark model was regressed using the new policy structure and policy implementation variables. The results of Models (1) and (3) in Table 7 showed that policy structure was statistically significant at the 1% level and the coefficient was positive, indicating that policy structure can significantly affect the satisfaction of farmers with GPPs. The results of Models (2) and (3) showed that policy implementation was statistically significant at the 1% level and the coefficient was positive, indicating that policy implementation affected the satisfaction of farmers with GPPs. This comprehensive analysis indicated that the conclusions of the benchmark regression were reliable.  
(2) Restricted-sample robustness test. People over 60 years old are considered elderly and are generally considered unsuitable for agricultural production and operation because of their aging physical condition [47]. Therefore, to test the robustness of the benchmark regression results, data samples over 60 years old were excluded. The estimation results are exhibited in Table 8. The results of the restricted samples were found to be more consistent with the full sample estimation results, indicating that the estimation results of the benchmark regression model were robust and the conclusions were reliable.  
(3) Changing the value of the core variable. The assignment of independent variables for policy structure and implementation was changed from the original 5-level scale to binary values, and the values of these variables were recalculated. The specific operation was to reset the values assigned as 1, 2, and 3 to 0, and to reset the values assigned as 4 and 5 to 1. The robustness test results after changing the values of the policy structure and policy implementation variables are shown in Table 9. Both the policy structure and policy implementation variables were found to be significant with positive regression coefficients, indicating that the regression results of the benchmark model were robust and the conclusions were relatively reliable.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variables** & **Model (1)** & **Model (2)** & **Model (3)** \\ \hline policy structure & 0.826 *** & & 0.805 *** \\  & (0.0427) & & (0.0623) \\ policy implementation & & 0.561 *** & 0.285 *** \\  & & (0.0394) & (0.0591) \\ \hline Control variable & Yes & Yes & Yes \\ Pseudo R2 & 0.2678 & 0.2092 & 0.2768 \\ \hline \hline \end{tabular}  
* Notes: *** represents statistical significance at the 1% level.  
\end{table}
Table 7: The estimation results after replacing the core independent variable.