## 3 Methodology
### Hot Spot Analysis: Getis-Ord \(G_{i}\)*  
The Getis-Ord \(G_{i}\)* was used to conduct hotspot analysis in order to identify the road accident hotspots' location based on the \(p\)-value, z-value, and \(G_{i}\)* function. \(G_{i}\)* is a highly reliable geostatistical technique that can be used to map clusters and identify statistically significant hotspots. Hotspot analysis successfully sets up necessary measures in places with one or more clustering patterns, such as road accidents. It helps to comprehend the likely reasons for those clustering patterns and to visualize the cluster locations and geographic range. The tool computes the \(G_{i}\)* metric for each feature present in a given dataset. The spatial clustering of elements exhibiting high or low \(p\)-values and z-scores is subsequently determined.  
The \(p\)-value stands for probability, meaning the probability that the observed spatial pattern resulted from a random process as determined by pattern analysis instruments. Once the \(p\)-value is extremely small, the null hypothesis is rejected because it is highly improbable that the observed spatial pattern resulted from random processes. Each feature is classified as a statistically significant hotspot if it exhibits a high value and is encompassed by other features with high values. Prior to conducting the spatial analysis, a confidence level was therefore determined. The levels of confidence in this research were 90%, 95%, or 99%. A statistically significant z-score is computed when the local sum of the characteristic and its neighbors deviates from the anticipated local sum by an amount that is not clarified by chance. \(G_{i}\)* is a z-score statistic; the greater the z-score (positive z-score), the denser the clustering of high values; the smaller the z-score, the reverse. The lower the z-score, the more low-value clustering (negative z-score).  
The analysis utilizing Getis-Ord \(G_{i}\)* commenced with a null hypothesis pertaining to accident severity index and spatial distribution, and complete spatial randomness with regards to accident severity index within the study area. Thus, it is feasible to ascertain whether to reject the null hypothesis, establish the level of confidence, and compute the z-scores and \(p\)-values for the index of accident severity. The user executed a spatial join operation to consolidate the accident severity indices that were associated with individual road segments. At present, it is feasible to generate a novel attribute field for the layer of the road network. The aforementioned field denotes the severity index of accidents that occurred on a specific segment of a roadway. The input of this attribute field was subsequently used to compute the hotspot function, specifically the Getis-Ord \(G_{i}\). The spatial relationship conceptualization was calculated using a fixed threshold distance of 1 km. A hotspot analysis (Getis-Ord \(G_{i}\)*) and detection of hotspots for road accidents was executed. The statistical formula for determining \(G_{i}\)* is given in Equations (3)-(5) [73]:  
\[G_{i}^{*}=\frac{\sum_{j=1}^{n}w_{ij}x_{j-\overline{X}}^{*}\sum_{j=1}^{n}w_{i,j} }{S\sqrt{\frac{\sum_{j=1}^{n}w_{ij}^{\overline{X}}(\sum_{j=1}^{n}w_{ij})}{n-1}}} \tag{3}\]  
\[\overline{X}=\frac{\sum_{j=1}^{n}x_{j}}{n} \tag{4}\]  
\[S=\sqrt{\frac{\sum_{j=1}^{n}x_{j}^{2}}{n}}-\overline{X}^{2} \tag{5}\]  
where, \(w_{i,j}\) is the weight between accident features \(i\) (first location) and \(j\) (second location), \(x_{j}\) is the attribute value of feature \(j\) (accident severity index), \(G_{i}\)* is a z-score statistic, \(\overline{X}\) is mean value, \(S\) is standard deviation, and \(n\) is the total features number.