## 2 Materials and Methods
### High/Low Clustering (G*) (Hot Spot Analysis)  
High/low clustering (Getis-Ord General G or G* test), also known as \"hot spot analysis\", was developed by [PERSON] ([PERSON], 1994). This test is a tool for measuring the value of some variables that cluster in certain areas. The null hypothesis states that there is no spatial clustering of feature values. This method can identify spatial cluster patterns in each region, thereby improving the interpretability of the results and facilitating policy implications. Equation (3) represents the mathematical representation of high/low clustering:  
\[G=\frac{\sum_{i}^{n}=1\sum_{j=1}^{n}w_{ij}x_{i}x_{j}}{\sum_{i}^{n}=1\sum_{j=1}^ {n}x_{i}x_{j}},\ \forall j\
eq i \tag{3}\]  
where \(x_{i}\) and \(x_{j}\) are the attribute values of variables in the interest area \(i\) and \(j\), respectively, and \(w_{ij}\) is the spatial weight matrix. When the test shows that the null hypothesis is rejected, it confirms the concentration of value and clustering.  
LM Test for Spatial Dependence (LM-Lag, LM-Error), LM Test for Random Effects, LM Test for Serial Correlation  
We conducted the LM test for spatial dependence to determine the most appropriate model for the dataset and to assess whether a lag or error model is more suitable. Based on the results, we can then select the specific model type to be used throughout the study.  
Table 5 shows that [PERSON]'s I statistic is 2.554, with a corresponding \(p\)-value of 0.01, which is less than 0.05. This indicates that the sample data exhibits spatial correlation. Al  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variable:** & & & & & \\
**Energy Consumption per Capita** & **Whole Region** & **BKK\&VIC, CE, EA, WE** & **NE** & **NO** & **SO** \\ \hline Moran’s I & 0.658 & 0.932 & 0.961 & 0.884 & 0.994 \\ \hline E(I) & \(-\)0.013 & \(-\)0.013 & \(-\)0.013 & \(-\)0.013 & \(-\)0.013 \\ \hline SE(I) & 0.088 & 0.091 & 0.094 & 0.094 & 0.089 \\ \hline Z(I) & 7.690 & 10.419 & 10.363 & 9.507 & 11.269 \\ \hline \(p\)-value & 0.001 & 0.001 & 0.001 & 0.001 & 0.001 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Moran’s I statistical test for the year 2022.  
though, the LM-Error and LM-Lag tests are insignificant. However, the results of Moran's I statistical test remain statistically significant, indicating that it is appropriate to apply a spatial econometric model to capture the spillover effects of variables influencing neighboring provinces. The choice of a spatial econometric model depends on the form of spatial dependence between units and the type of spatial interaction effect that is present. Although taking the Dynamic Spatial Durbin model (DSDM) as a benchmark model is theoretically reasonable, further tests should be conducted to confirm this. We initially estimated several spatial econometric models to identify the most suitable one for this study, based on Equation (5), using the AIC (Akaike information criterion) and BIC (Bayesian information criterion) values as primary criteria for model comparison. The results show that the Spatial Lag Model (SLM) has the lowest AIC and BIC values (AIC: \(-1840.59\) and BIC: \(-1796.36\)), while the Spatial Error Model (SEM) has an AIC of \(-1823.54\) and BIC of \(-1779.31\), and the Spatial Durbin Model (SDM) has an AIC of \(-1830.87\) and BIC of \(-1751.26\). Therefore, the SLM method is employed to estimate the results and address the research questions of this study. The Spatial Lag Model (SLM) captures substantive spatial dependence by directly incorporating spatial interaction into the model rather than merely correcting for the potentially biasing effects of spatial autocorrelation that may arise from the use of spatial data or nonlinear parametric restrictions. This makes the SLM approach more suitable than the SEM or other spatial econometric models (e.g., SDM and SDEM) [51; 67]. Additionally, the Hausman test rejects the null hypothesis of the random-effects model, indicating that the fixed-effects model is more appropriate for these datasets.