## 4 Results
### Implication of the Identified Components  
To examine the weights assigned to each variable in the dataset for each principal component, we delve into the analysis of component loading in PCA. The PCA component displays the component loading values, as depicted in Figure 7a. A total of 157 village datasets are represented by blue dots, with coordinates reflecting the score of each observation for the two principal components. All eleven variables are represented by red lines, with the direction and length of each line indicating the contribution of that variable to the two principal components.  
Figure 6: Variable importance plot using the OOB predictor (red color represents correlation coefficients greater than 0.7, gray color represents correlation coefficient less than 0.7).  
Figure 7: Biplots: (**a**) PCA; (**b**) FA. (blue dots represent the original variables, while red lines represent the directions and magnitudes of the principal components).  
The primary principal component, aligned along the horizontal axis, demonstrates positive coefficients for all nine variables, explaining why the vectors representing these variables point towards the right half of the plot. Notably, Factors 1, 3, 7, and 11 exhibit the most substantial coefficients in the first principal component, approximately greater than 0.3, while the component loadings for other factors are less than 0.3. On the vertical axis, the second principal component showcases positive coefficients for variables such as Factors 1, 6, 9, 10, and 11, along with negative coefficients for the remaining variables. In this study, the first principal component (PC1) accounts for 58% of the variance, while the second principal component (PC2) accounts for 13% of the variance. Together, PC1 and PC2 explain 71% of the total variance. This means that these two components capture 71% of the original variability present in the dataset.  
This study further explores the correlation of these factors using FA. The FA results, as shown in Figure 6(b), reveal the predicted factor scores obtained through FA. Results obtained demonstrate that population-related factors are positioned near the second-factor axis, while building-related factors are closely aligned with the first axis. This enhances the interpretation of these rotated factors as \"quantitative ability\" and \"qualitative ability\". Instead of plotting the variables on different sets of rotated axes, an alternative approach is to overlay the rotated axes onto an unrotated biplot (as depicted in Figure 6(b)) to gain a clearer understanding of the relationship between the rotated and unrotated solutions.  
The FA results suggest that villages with higher fire density tend to concentrate in areas with a higher proportion of tertiary sectors of the economy (first quadrants). In summary, while both PCA and FA are utilized for dimensionality reduction, PCA primarily focuses on summarizing variance, and its components may lack clear interpretations. On the other hand, FA aims to provide an explanatory model for observed correlations by identifying underlying latent factors with meaningful interpretations.  
Subsequently, this study performs FA to explore the characteristics of these fire-related factors. A biplot of the eleven variables on the rotated factors demonstrates the effect of varimax rotation, as illustrated in Figure 8. Figure 7(a) indicates that Factors 2 to 5 are positioned closest to the first factor axis, while Factors 9 to 11 are nearest to the second axis. These two rotated factors are likely best interpreted as \"population-related features\" and \"economic-related features\". Figure 7(b),c yield similar results, demonstrating the advantages of FA, which introduces the concept of latent factors. The connection between latent factors is based on their shared objective of decreasing the number of variables while preserving significant information.  
Figure 8: \(Cont.\)