## 2 Theoretical Foundations and Development of Hypotheses
### Structural Model  
Having concluded the analysis of the measurement model, we analyzed the structural model. Firstly, the possible existence of multicollinearity between the antecedent variables of the endogenous construct was tested. According to [PERSON] et al. (2018), there exist signs of multicollinearity when the VIF indicator is above 5. In the structural model proposed problems of multicollinearity do not exist. After this, a Bootstrapping (5000 samples) was done. This provides both the t values and the confidence intervals which allow the evaluation of the statistical significance of the relations. The empirical evidence reveals that there exists a significant relation between the three impact dimensions analyzed (economic, environmental, and social) and the satisfaction with the public administration of tourism, so hypotheses H1, H2, and H3 are accepted. Table 4 shows the direct effects included in our research model.  
The application of blindfolding enables evaluating the predictive importance of the constructs. When carrying out blindfolding procedures, all the Q2 values are above zero, which backs the predictive relevance for the endogenous constructs (Table 5). Values higher than 0.25 (0.325) depict medium predictive accuracy of the PLS path model ([PERSON], 2018).  
The coefficient of determination (R2) is also examined to evaluate the explanatory power for the endogenous constructs and indicates the quantity of variance of a construct which is explained by the predictive variables of this endogenous construct in the model ([PERSON], 2018). Therefore, in the model proposed the Economic Impact explains 41.87% of the satisfaction with the public administration of tourism, the environmental impact 9.35% of it, and the socio-cultural impact explains 13.46% of this satisfaction (Table 5).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Path** & **P Values** & **T statistics** &
\begin{tabular}{c} **Confidence** \\ **Interval** \\ \end{tabular} & **f2** & **Supported** \\ \hline ECON -\(>\) SAT & 0.538 & 0.000*** & 7.863 & [0.395; 0.666] & 0.306 & Yes \\ \hline ENV -\(>\) SAT & 0.173 & 0.000*** & 3.617 & [0.086; 0.271] & 0.061 & Yes \\ \hline SC -\(>\) SAT & 0.197 & 0.003** & 2.985 & [0.071; 0.328] & 0.046 & Yes \\ \hline \hline \end{tabular}  
* p \(<\) 0.001, *
* p \(<\) 0.01,
* p \(<\) 0.05, ns: not significant t (0.05; 4999) = 1.64791345; t (0.01; 4999) = 2.333843952; t (0.001; 4999) = 3.106644601 Sig. at 0.05.  
\end{table}
Table 4: Results of the structural model.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Fronell–Larker Criterion**} & \multicolumn{4}{c}{**Hetetrotrait–Monotrait Ratio HTMT**} \\ \hline  & ECON & ENV & SAT & SC & ECON & ENV & SAT & SC \\ ECON & 0.814 & & & & & & \\ ENV & 0.524 & 0.786 & & & 0.541 & & \\ SAT & 0.779 & 0.541 & 0.747 & & 0.680 & 0.555 & & \\ SC & 0.762 & 0.436 & 0.682 & 0.721 & 0.843 & 0.455 & 0.791 & \\ \hline \hline \end{tabular}  
* Note: ECON: Economic Impact; ENV: Environmental Impact; SAT: Satisfaction with the Public Administration of Tourism/SC: Social Impact.  
\end{table}
Table 3: Measurement Model. Discriminant Validity.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \(\mathbf{R^{2}}\) & \(\mathbf{Q^{2}}\) & **Direct effect** & **Correlations** &
\begin{tabular}{c} **Variance** \\ **explained** \\ \end{tabular} \\ \hline Satisfaction with tourism & 0.647 & 0.325 & & & \\ H1: Positive Economic Impact & & & 0.538 & 0.779 & 41.87\% \\ H2: Negative Environmental Impact & & & 0.173 & 0.541 & 9.35\% \\ H3: Positive Socio-cultural Impact & & & 0.197 & 0.682 & 13.46\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: Effects on the endogenous variables.  
All indicator's Q2-predict values are positive and comparing the RMSE values from the PLS-SEM analysis with the naive LM benchmark (Table 6), we find that the PLS-SEM analysis produces lower prediction errors for all the indicators. Therefore, high predictive power was achieved [52].