Effectiveness is the comparison between results and objectives. Therefore, to assess the effectiveness of village fund management, it is necessary to compare actual expenditures with budgeted expenditures. Therefore, analyzing the effectiveness of village fund utilization involves assessing the ratio of actual expenditures to budgeted expenditures (Arifin et al., 2020)(Watts et al., 2019). The effectiveness of village fund utilization is measured using the following formula:

The resulting percentage is then assessed using the effectiveness standards stipulated in the Decree of the Minister of Home Affairs No. 690.900-327 of 1996 concerning assessment criteria and financial performance. According to these standards, a comparison result above 100% is classified as very effective, while a result between 90% and 99.9% is considered effective. A result between 80% and 89.9% is classified as quite effective, whereas a result between 60% and 79.9% is considered less effective. Finally, a result below 59.9% is classified as not effective.

To examine the relationship between village fund utilization, poverty, and village development performance, researchers used Geographically Weighted Regression (GWR) analysis. The GWR analysis model is a global regression analysis model that is transformed into a weighted regression analysis model ((Khedmati Morasae et al., 2024); (Sifriyani et al., 2024)). The fundamental difference between GWR analysis and global regression analysis is that GWR analysis produces local parameter estimates for each observation location. In contrast, global regression analysis provides general parameter estimates across all observation locations. In GWR analysis, because parameter values are determined at each geographic location, the regression parameter values vary across geographic locations. Consequently, the results of the GWR analysis describe the variation in regression parameter values across geographic regions. If the regression parameter values are constant across geographic regions, then the GWR model becomes a global model or ordinary least squares (OLS) regression (Khedmati Morasae et al., 2024). This implies that each geographic region has the same model. One of the advantages of the GWR model is its ability to account for spatial heterogeneity, allowing relationships between variables to vary across geographic locations. This provides an advantage over global regression approaches, which assume that the estimated coefficients are constant across locations. In the GWR model, the regression coefficients are therefore allowed to vary geographically, capturing differences in the relationships between the predictor and response variables from one location to another. The basic GWR model can be expressed as follows:

In Equation (2), Y_i represents the response variable at location i, where i = 1, 2, ..., n, while X_ik denotes the k-th predictor variable at location i. The coordinates (u_i,v_i) represent the longitude and latitude of location i. The coefficient β_k (u_i,v_i) represents the regression coefficient of predictor k at location i, allowing the effect of each predictor to vary across geographic locations. Finally, ε_i represents the error term, which is assumed to have a mean of zero and a constant variance of σ², with the errors assumed to be independent and normally distributed.

In this study, GWR analysis was used to examine the relationship between the effectiveness of village funds, poverty and rural development, resulting in four quadrants, namely: Quadrant I (high-low), Quadrant II (high-high), Quadrant III (low-high) and Quadrant IV (low-low) ((Chen et al., 2023); (Wang et al., 2024)).

One method for assessing spatial relationships is to use the Moran Index. The Moran test aims to determine spatial dependence or autocorrelation between observations or locations, meaning that the characteristics of a village will influence (or be influenced by) the characteristics of surrounding villages. The Moran Index is used to describe and explain spatial distribution, identify clusters, and determine outliers. Positive autocorrelation indicates similar values among adjacent locations and a tendency to cluster. Negative autocorrelation indicates that adjacent locations have different values and tend to be dissimilar. The formula for calculating spatial autocorrelation using the Moran Index is as follows: (Lee & Wong, 2001):

In Equation (3), I represents the Moran Index, while n denotes the number of villages observed. The terms x_i and x_j represent the observed values for villages i and j, respectively, where village j is adjacent to village i. The term represents the average value of the observed variable across all villages, while w_ij represents the spatial weight between villages i and j.

The hypotheses for the Moran Index are formulated as follows: H₀: I = 0, indicating no spatial autocorrelation among the villages, and H₁: I ≠ 0, indicating the presence of spatial autocorrelation among the villages. The expected value of the Moran Index is given by:

Spatial autocorrelation between locations occurs if:

where Var is the variance of Moran's I, I₀ is the expected value of Moran's I, and I is the Moran's I statistic. Three categories can be used to categorize the values or patterns seen in the Moran Index: clustered, random, and scattered. When |Z-score| > Z_α/2, the null hypothesis (H₀) rejected. The Moran’s I statistic ranges from -1 to 1. A positive spatial autocorrelation indicates a clustered pattern when I > I₀, whereas a negative spatial autocorrelation indicates a dispersed pattern when I < I₀(Weng et al., 2022).

The effectiveness of village spending in Belitung Regency is measured by comparing the target and actual village spending in several areas, namely village governance, village development, community development, and village community empowerment. Overall, village fund management by village governments in Belitung Regency is considered quite effective, with an average effectiveness of 83 percent. By sector, the highest absorption is found in village governance, with an average of 91 percent, followed by village development at 86 percent. The lowest absorption is found in village community empowerment, which only reaches 46 percent.

The number of poor households is used as the primary indicator to describe poverty levels in each region. This data is then analyzed using the Moran Index to determine whether there is a clustered, dispersed, or random spatial distribution of poverty. This information is then used to assess the effectiveness of village fund utilization in poverty reduction based on the spatial patterns identified.

Based on an analysis conducted by (Hariyanto et al., 2023), it is known that the Moran Index results indicate that the distribution of poverty levels in Belitung Regency is random, with a spatial autocorrelation value of -0.013404 and an expected index value of -0.024390. This indicates that there is no poverty clustering between adjacent villages. This condition is influenced by the characteristics of village areas that are scattered and not strongly connected to each other, so that spatial continuity and connectivity between regions are relatively low. Thus, the poverty level in a village in Belitung Regency is not directly influenced by the poverty conditions in neighboring villages.

Based on 2022 data from the Ministry of Villages, Development of Disadvantaged Regions and Transmigration (Kemendes PDTT), the village development status based on the Village Development Index (IDM) in Belitung Regency is divided into three categories: 9 independent villages (21.43 percent), 28 developed villages (66.67 percent), and 5 developing villages (11.90 percent). This composition indicates that the government still needs to optimize the management and development of village resource potential to encourage a more equitable improvement in village status. Furthermore, strengthening various supporting components of village development, particularly economic, ecological, and social aspects, is needed to ensure sustainable village development achievements.

From the results of the analysis above, an analysis of the relationship between the effectiveness of village fund utilization and poverty levels was then carried out, which was divided into four quadrants, including: Quadrant I shows that high effectiveness in utilizing village funds is correlated with low poverty levels in the village. Quadrant II explains the high effectiveness in utilizing village funds, but also the high level of village poverty. Quadrant III shows low effectiveness in utilizing village funds, combined with high levels of village poverty. Quadrant IV explains the low effectiveness in utilizing village funds, but also the low level of poverty.

The average effectiveness of village fund utilization in Belitung Regency is 78.58%, while the average number of poor households per village is 407. Correlation analysis using EViews indicates a very weak positive relationship between the effectiveness of village fund utilization and the poverty rate, with a correlation coefficient of 0.02. This suggests that differences in the effectiveness of village fund utilization are only weakly associated with differences in poverty rates across villages, indicating that other factors also contribute to variations in poverty levels ((Burke & Siyaranamual, 2019); (Hariyanto et al., 2023)). The spatial distribution of villages across the four quadrants reveals considerable variation in this relationship. Quadrant I comprises 16 villages (38.09%) where village fund utilization is relatively effective and poverty rates are low, suggesting a favorable development condition. Quadrant II includes 6 villages (14.29%) where village fund utilization is effective but poverty rates remain high, indicating that effective fund utilization has not necessarily translated into lower poverty. Quadrant III consists of 11 villages (26.19%) characterized by low effectiveness in village fund utilization and high poverty rates, representing villages that may require greater attention. Finally, Quadrant IV comprises 9 villages (21.43%) where fund utilization is less effective but poverty rates remain low. The classification of villages based on the effectiveness of village fund utilization and poverty levels is presented in Table 1 and Figure 5.

Based on the analysis, the relationship between the effectiveness of village fund utilization and rural development performance can be determined. The results indicate that this relationship falls into four quadrants: Quadrant I, Quadrant II, Quadrant III, and Quadrant IV. Quadrant I indicates that high effectiveness in village fund utilization is not followed by improved performance, due to low levels of rural development performance (IDM).Quadrant II describes high effectiveness in village fund utilization, followed by high levels of rural development performance (IDM).Quadrant III describes low effectiveness in village fund utilization but high levels of rural development performance (IDM).Quadrant IV indicates that low effectiveness in village fund utilization is also accompanied by low levels of rural development performance.

The average effectiveness of village fund utilization in Belitung Regency is 78.58%, while the average Village Development Index (IDM) is 0.7631. The correlation analysis indicates a very weak positive relationship between the effectiveness of village fund utilization and rural development performance, with a correlation coefficient of 0.003. This value is close to zero, suggesting that the effectiveness of village fund utilization is only weakly associated with variations in rural development performance across villages. The distribution of villages across the four quadrants further illustrates the variation in this relationship. Quadrant I comprises 12 villages (28.57%) where village fund utilization is highly effective but rural development performance remains low. Quadrant II includes 10 villages (23.81%) where both fund utilization effectiveness and rural development performance are high. Quadrant III consists of 11 villages (26.19%) where fund utilization effectiveness is low despite relatively high rural development performance. Finally, Quadrant IV comprises 9 villages (21.43%) where both fund utilization effectiveness and rural development performance are low. The classification of villages based on these two indicators is presented in Table 2 and Figure 6.

From the analysis, it is clear that the relationship between rural development performance and poverty levels in Belitung Regency is spread across all quadrants: Quadrant I, Quadrant II, Quadrant III, and Quadrant IV (Chen et al., 2022)(Nugroho, 2010). Quadrant I shows that high or good rural development has an impact on reducing poverty levels in villages. Quadrant II explains high rural development performance (IDM) but also high poverty levels in villages. Quadrant III describes low rural development performance, followed by high levels of rural poverty. In Quadrant IV, it is described that low rural development performance is accompanied by low levels of poverty in villages.

The average rural development performance (IDM) in Belitung Regency is 0.7631, while the average number of poor households per village is 407. The analysis of the relationship between rural development performance and poverty indicates a very weak positive correlation, with a correlation coefficient of 0.007. The reported coefficient is close to zero, suggesting that rural development performance is only weakly associated with differences in poverty levels across villages. The distribution of villages across the four quadrants further illustrates the variation in this relationship. Quadrant I comprises 12 villages (28.57%) with high rural development performance and low poverty levels. Quadrant II includes 8 villages (19.05%) with both high rural development performance and high poverty levels, indicating that relatively strong development performance does not necessarily coincide with low poverty. Quadrant III consists of 8 villages (19.05%) characterized by low rural development performance and high poverty levels. Finally, Quadrant IV comprises 14 villages (33.33%) with low rural development performance and low poverty levels. The classification of villages based on rural development performance and poverty levels is presented in Table 3 and Figure 7.

Based on the relationships among village fund utilization effectiveness, poverty, and rural development performance (IDM), eight village typologies were identified in Belitung Regency. These typologies reflect different combinations of development conditions and corresponding development priorities. The results of this typological classification can serve as a basis for recommending the development of priority villages (Anser et al., 2023)(Li et al., 2023)(Stasi et al., 2024)(Ullah et al., 2024).

Typology A comprises villages with low village fund utilization effectiveness, high poverty rates, and low rural development performance. These villages are assigned the highest development priority. Typology B consists of villages with low fund utilization effectiveness and high poverty rates and is assigned the second-highest priority. Typology C includes villages with low fund utilization effectiveness and low rural development performance, corresponding to the third-highest priority. Typology D, assigned the fourth-highest priority, comprises villages with high poverty rates and low rural development performance. Typology E consists of villages with low fund utilization effectiveness and is assigned the fifth-highest priority, while Typology F, characterized by high poverty rates, is assigned the sixth-highest priority. Typology G comprises villages with low rural development performance and is considered a lower development priority. Finally, Typology H consists of villages in relatively stable conditions, for which development efforts should focus on maintaining and improving their current conditions. The characteristics and distribution of the eight village typologies are presented in Table 4 and Figure 8.