The most crucial aspect of any research project is the collection and extraction of data. The process of extracting data was both time-consuming and demanding. Data collection for the vehicle-to-pedestrian study was conducted. The accident data for this study was collected from the Madhya Pradesh Road Development Corporation (MPRDC) and comprises approximately 6000 entries. The dataset includes detailed information on various variables related to road accidents, such as the age of the individuals involved, age of the vehicles, type of vehicles, gender of the individuals, time of the day when the accident occurred, type of violation, surface condition at the time of the accident, type of injury sustained, and other relevant details. The data collection process involved accessing MPRDC's records and databases, which provided comprehensive information on road accidents in the region. The dataset was collected over a specified period to ensure a representative sample and comprehensive coverage of accident incidents. This dataset is crucial for understanding the factors contributing to road accidents in Madhya Pradesh and forms the basis for the subsequent analysis using latent class analysis to identify patterns and trends within the data.

While the dataset obtained from the Madhya Pradesh Road Development Corporation (MPRDC) and the Accident Response System offers valuable insights into vehicle-to-pedestrian crashes, it is important to note that reporting coverage may be more robust along national highways, state highways, and major district roads. This may lead to potential underreporting or omission of crashes in dense urban neighbourhoods or remote rural areas where formal reporting systems are limited. As such, the dataset might exhibit some geographic bias toward better-connected road networks.

Crash data for this study is obtained from Madhya Pradesh Road Development Corporation and Accident Response System database, limiting the scope of pedestrian accidents between 2019 to 2023. To prevent redundancy variables like pedestrian city, state, and zip code are dropped for clarity. The study focused on the factors that influence the severity of vehicle-to-pedestrian collisions, including pedestrian characteristics such as age, gender, availability of footpath, traffic violations, number of injuries and severity, crash specifics like time, location, surface condition, vehicle type, and environmental factors such as season, weather, lighting, and rural/urban setting.

To assess geographic variation, location-related attributes were extracted to categorize crash sites as urban, suburban, or rural based on administrative tagging and road function classification. Preliminary analysis indicates that approximately 41.2% of recorded crashes occurred in rural regions, 38% in urban zones, and the remaining 20.3% in suburban corridors. This provides a reasonable distribution across different settlement typologies in the state, although the likelihood for reporting bias in lower density or informal areas is acknowledged. Table 1 summarizes the distribution of pedestrian crash outcomes by key demographic; behavioural, vehicular, and roadway-related variables. Percentages under each injury severity category represent the proportion of crashes within that subgroup resulting in no injury, minor injury, or grievous injury.

Several steps are carried out in the data analysis stage to ensure the reliability and usability of the dataset. The data was checked for accuracy and consistency to confirm its reliability. This involved identifying and correcting errors or inconsistencies in the dataset. Once verified, the data was converted into numerical format by encoding categorical variables. For instance, the time-of-day variable was encoded as: "morning" = 1, "afternoon" = 2, "evening"=3, and "night" = 4. This standardization step facilitated seamless processing in statistical software.

After encoding, the data was imported into IBM SPSS Statistics 27 for descriptive analysis and into Jamovi 2.3.28 software for latent class clustering. SPSS was used to test the internal consistency and reliability of the dataset, ensuring the validity of the conclusions drawn. Once verified and coded, the dataset was analysed in Jamovi using Latent Class Analysis (LCA). Jamovi is a user-friendly statistical software that facilitates latent class identification and sub-group discovery from within a set based on observed variables' pattern. The whole process facilitates uncovering patterns or underlying structures that otherwise may lie hidden within data, shedding insight into processes or mechanisms underlying them. LCA was chosen because it is a model-based probabilistic approach particularly well-suited for identifying latent (unobserved) subpopulations in heterogeneous data based on observed categorical or mixed-type variables. Unlike K-means, which assumes clusters are spherical and equidistant in feature space, LCA does not require such geometric assumptions and can model complex, non-linear relationships among variables. Additionally, LCA provides fit indices (e.g., AIC, BIC) to determine the optimal number of classes, enhancing model interpretability and statistical robustness. Given that pedestrian crash data involves a mixture of categorical and ordinal variables (e.g., road type, time of crash, vehicle type, severity level), and is affected by underlying unobserved heterogeneity (e.g. behavioural or environmental factors not directly measures), LCA offers a more appropriate and interpretable clustering framework. This is consistent with best practices followed in recent traffic safety literature (e.g. Sun et al., 2019; Zhu et al., 2023).

The algorithms to implement Random Forest have also been achieved using software packages like Python. These machine learning techniques are further used to analyze the data and find the important predictors or variables that are responsible for the outcome of interest. Overall, the data analysis phase is a series of steps to ensure reliability and validity of the data and to find the hidden patterns and relationships in the dataset. With the judicious use of statistical analysis and machine learning techniques, the factors influencing road accidents can be identified, and eventually strategies to enhance road safety can be evolved.

Analyzing the data proved to be a formidable task, requiring careful attention to detail and a thorough understanding of the dataset. The reliability of the collected data was paramount, as any inaccuracies could jeopardize the integrity of the entire analysis. Ensuring the data's reliability involves meticulous validation processes and rigorous checks to identify and rectify any errors or inconsistencies. Furthermore, the complexity of the data added another layer of difficulty to the analysis process. The dataset encompassed a wide range of variables, each requiring careful consideration and interpretation. This complexity underscored the importance of a systematic and structured approach to data analysis. Despite these challenges, a meticulous and methodical approach to data analysis ensured that the process was conducted smoothly and efficiently. By prioritizing the reliability of the data and employing a systematic analytical approach, the study was able to derive meaningful and actionable insights from the dataset, contributing to a robust and comprehensive research outcome.

Latent Class Analysis (LCA) is a statistical method used to identify underlying subgroups or "classes" within a population based on their responses to a set of observed categorical variables. This method is widely used in various fields, including psychology, sociology, and marketing, to uncover hidden patterns in data. In the context of this discussion, the process of conducting LCA using the Jamovi software involves several steps. Firstly, the data must be prepared by coding it into a numeric format. This step is crucial as LCA requires categorical data to be represented numerically for analysis. Once the data is coded, the next step is to import it into Jamovi software. This is typically done using an Excel file, which contains the coded data. Upon importing the data, the variables need to be configured based on their nature. Variables can be nominal, ordinal, or continuous, and this information helps the software understand the nature of the data and how it should be analyzed.

The provided elbow plot (Figure 2) for latent class analysis (LCA) determines the optimal number of classes using several fit indices: AIC, BIC, ABIC, and CAIC. The plot shows a significant decline in fit index values when moving from one class to two classes, indicating a considerable improvement in model fit. This sharp drop suggests that a two-class model captures much of the data’s heterogeneity. As the number of classes increases from two to three, the fit indices—AIC, BIC, ABIC, and CAIC—either slightly decrease or remain relatively stable, indicating further improvement, though less dramatic (Table 2). This suggests that a three-class solution provides a better fit without overcomplicating the model. Thus, considering the balance between model fit and complexity, the optimal number of classes is determined to be three. This helps in effectively capturing the underlying structure of the data while maintaining a parsimonious model.

Figure 3 presents the conditional probabilities of key categorical variables across the three latent classes identified through Latent Class Analyses. The X-axis includes multiple relevant crash-related variables – such as vehicle type, road type, and number of lanes, surface conditions, speed limit, road features, road junctions, and time of day, injury type, traffic violations, and traffic conflict-each broken down by category.

Class 1: Class 1 is characterized by a higher probability of minor injuries among its members. The population of this class is 27.7%. Around 60.1% of this class group have minor injuries. This group is generally less hazardous due to effective traffic control measures in place. Traffic control in these areas is typically managed using traffic signals or stop signs, particularly at staggered and four-armed junctions. These controls help reduce the severity of accidents, resulting in fewer severe injuries and a predominance of minor injuries. Members of this class benefit from systematic and structured traffic management, which contributes to a safer environment and minimizes the risk of more serious injuries.

Class 2: Class 2 is distinguished by well-managed traffic control, which helps to provide a more secure driving environment. The population of this class is 8.7%. Effective traffic safety measures are seen in the 32.8% of events in this class that ended without any injuries. Three wheelers acted for 37.7% of all vehicles involved in crashes within this latent class, indicating that pedestrian collisions involving three-wheelers were a prominent feature of this group. Four wheelers were also involved in 19.5% of crashes. In order to ensure that a sizable percentage of crashes do not result in injuries, structured traffic control measures—likely to include appropriate signage, lane management, and enforcement of traffic rules—help to lower the overall severity of accidents.

Class 3: The population of this class is 63.5%. Class 3 exhibits a heightened likelihood of severe accidents, with 59.31% of incidents resulting in grievous injuries. The predominant portion of collisions within this category occurs in regions featuring less than two lanes, indicative of narrow or restricted road conditions contributing to such occurrences. A notable 94.24% of accidents within this class happen due to the loss of vehicle control, emphasizing challenges associated with vehicle maneuverability and stability. Moreover, 90.9% of incidents in this class are attributed to over speeding, accentuating the pivotal role of excessive velocity in escalating accident severity. This class typifies high-risk situations characterized by inadequate road infrastructure and lax speed regulation, culminating in severe outcomes (Figure 3).

Table 3 presents the conditional probabilities of key categorical variables across the three latent classes identified through Latent Class Analysis. These values indicate the likelihood that a crash with a given characteristic (e.g. vehicle type, road type, violation) falls into each latent class. For example, Class1 is more associated with two-wheeler vehicles (705) and straight roads (855), while Class 2 shows higher probabilities for truck/bus involvement (355) and better road surface conditions (555). Class 3 is affected by grievous injuries (59%), vehicle –pedestrian conflicts (55%), and higher presence of district roads (40%) and curved road features (20%). This table compliments Figure 3 by providing a detailed numerical summary, enabling precise comparisons across the latent classes and helping interpret the unique crash profiles each class represents. Table 4 presents the distribution of vehicle-to-pedestrian crash records across the three latent classes identified through Latent Class analysis (LCA). Cluster 1 accounts for 27.63% of the dataset, comprising 1687 crashes, suggesting a moderate share of incidents with potentially distinct characteristics such as controlled environments or specific vehicle types. Cluster 2, the smallest segment, represents 8.89% of the total crashes (543 record), indicating a relatively rare crash profile that may be associated with; low-risk scenarios or well-managed infrastructure. In contrast, Cluster 3 dominates the dataset, making up 63.49% of all cases with 3876 crashes. This class likely encompasses the most hazardous crash conditions, possibly linked to poor infrastructure, higher speeds, or other risk-intensive factors. The segmentation highlights the heterogeneity of crash context and provides the foundation of class-specific safety analysis and intervention.

The random forest algorithm is a powerful ensemble learning technique used for classification and regression tasks. Developed by Leo Breiman and Adele Cutler, it combines the predictions of multiple decision trees to improve accuracy and control overfitting. Breiman introduced the Random Forest (RF) classifier, which is composed of a large ensemble of individual, uncorrelated decision trees working together to make predictions. These trees are generated using a bootstrap aggregation (bagging) method, where subsets of the training data are created with replacement. About two-thirds of the samples, known as in-bag samples, are used to train the trees, while the remaining one-third, known as out-of-bag samples, are used in an internal cross-validation (CV) procedure. This CV process helps the algorithm estimate the out-of-bag error and develop a reliable RF model. Unlike some other decision tree algorithms, there is no pruning involved. Additionally, RF employs randomness by considering a random subset of features for each split. By constructing many trees, the algorithm produces a model with high variance and low bias. Once the RF is built, it predicts the class of a new observation by averaging the class votes from all the decision trees, selecting the class with the highest number of votes. The dataset used in this analysis comprises 6104 observations and 16 variables. These features include both numerical and categorical variables such as age, gender, type of injury, road type, speed limit, parts of the day, number of persons injured, lanes, surface condition, road features, type of vehicle, etc. Prior to modelling, the data underwent preprocessing steps, including missing value imputation, encoding categorical variables, and normalization of numerical features. In the process of data collection and preparation, various input features are gathered to construct a comprehensive understanding of the factors influencing the outcome. These features encompass a wide array of variables including Parts of the Day, Number of Persons Injured, Number of Vehicles Involved, number of lanes, the prevailing Surface Condition of the road, the classification of the Road Type, Speed Limit, Road Features, Road Junctions, the type of Traffic Control, Vehicle Types involved, the Age of Vehicles, Gender of individuals involved, and Type of Traffic Violation, Age. Following the comprehensive collection of these input features, the target variable, 'type of injury', is identified as the output feature. This variable serves as the focal point of predictive modelling, representing the nature and severity of injuries sustained in vehicular incidents. Subsequently, to facilitate effective model training and evaluation, the dataset is partitioned into two distinct subsets: a training set and a testing set. This partition ensures that the model can learn from a portion of the data and be evaluated on unseen data, thus enabling a robust assessment of its performance. The training subset comprises 75% of the data, providing an ample amount for model learning, while the testing subset encompasses the remaining 25%, allowing for rigorous evaluation and validation of the trained model's predictive capabilities.

To optimize the performance of the Random Forest Classifier, a Grid Search method was employed for hyper parameter tuning. The grid search systematically explored combinations of key parameters such as “n_estimators (100 to 300)”, “max_depth (5 to 25)”, “min_samples_split, (2, 5, 10)”, and “max_features (‘sqrt’, ‘log2’, or a fixed number)”. The model was trained and validated using a 5-fold cross-validation strategy on the training set. This approach allowed the model to be trained on different data subsets and validated on unseen portions iteratively, enhancing generalizability and reducing over-fitting. The final model was selected based on average F1-score and classification accuracy across folds, and its performance was then evaluated on the independent test set. These steps ensured the model’s robustness and the reliability of the reported classification metrics (accuracy: 88%, precision: 97.2%, recall: 89.2%).

Performance of the model can be evaluated from the confusion matrix. To thoroughly assess the model's performance, a 3x3 confusion matrix was employed. This matrix is instrumental in categorizing the outcomes of predictions across three distinct classes. It provides a detailed breakdown of true positives, false positives, and false negatives for each class, enabling a clear understanding of the model’s accuracy, precision, recall, and overall classification effectiveness. By examining this matrix, we gain valuable insights into the model's strengths and weaknesses, guiding further refinement and optimization of our classification approach. The confusion matrix obtained from the Random Forest Classifier, representing the classification performance on our dataset, is as follows: Here Variable A is grievously injured, B is Minor Injury, C is No injury.

The matrix is structured such that each row represents the instances in an actual class, and every column represents the instances in a predicted class (Table 5). The diagonal elements of the matrix represent correct classifications, and the off-diagonal elements represent misclassifications. Interpretation: Class A (Positive): Out of 847 instances of Class A, 823 were correctly classified as Class A (True Positives), 23 were misclassified as Class B (False Negatives), and 1 was misclassified as Class C (False Negatives). Class B Negative Out of 603 instances of Class B, 503 are correctly classified as Class B (True Negatives), and 100 are misclassified as Class A (False Positives), and there are no misclassifications of Class C. Class C (Negative): Among 76 instances of Class 3, 28 were correctly classified as Class 3 (True Negatives), 7 were misclassified as Class 1 (False Positives), and 41 were misclassified as Class 2 (False Positives). Precision: Precision is the degree of correctness of the positive predictions made by the classifier. It is defined as the ratio of true positives to the sum of true positives and false positives.

(1) Precision=TPTP+FP

Precision measures the accuracy of positive predictions made by the classifier. It is calculated as the ratio of true positives to the sum of true positives and false positives. For our classifier, precision is approximately 97.2%.

Recall (Sensitivity): Recall measures the proportion of actual positives that were correctly identified by the classifier. It is calculated as the ratio of true positives to the sum of true positives and false negatives.

(2) Recall=TPTP+FN

Recall measures the proportion of actual positives that were correctly identified by the classifier. It is calculated as the ratio of true positives to the sum of true positives and false negatives. The recall for our classifier is approximately 89.2%.

F1 Score: The F1 score is the harmonic mean of precision and recall, providing a balance between the two metrics. It is calculated as:

(3) F1 Score=2xPrecisionxRecallPrecision+Recall

The F1 score is the harmonic mean of precision and recall, providing a balance between the two metrics. It accounts for both false positives and false negatives. The F1 score for our classifier is approximately 93.1%.

Accuracy: The total number of correct predictions (sum of the diagonal elements) is 823+503+28=1354

The total number of instances in the dataset is the sum of all elements in the confusion matrix, which is 823+23+1+100+503+0+7+41+28=1524

Therefore, the accuracy of the Random Forest Classifier is calculated as:

(4) Accuracy=13541524≈0.888

This indicates that the classifier achieves an accuracy of approximately 88.8%, implying that it correctly classifies 88.8% of all instances in the dataset.

Moreover, Figure 4 shows how crucial each independent parameter is in establishing possible results depending on different variables. It provides a clear visual representation of the ways in which many factors affect the severity of injuries. The variables that have the most influence in vehicle-to-pedestrian crashes include age, vehicle age, road features, and the number of wounded individuals, as illustrated in Figure 4. On the other hand, in this case, gender and surface condition are thought to be less significant determinants. This graphic emphasizes the variables' hierarchical importance and the crucial part they play in determining how situations of this kind turn out. Figure 6 offers a thorough summary that facilitates comprehension of the complex nature of vehicle crashes involving pedestrians and provides information that can guide preventative and mitigating measures.

The variables that have the most influence in vehicle-to-pedestrian crashes include age, vehicle age, road features, and the number of wounded individuals, as illustrated in Figure 4. On the other hand, in this case, gender and surface condition are thought to be less significant determinants. This graphic emphasizes the variables' hierarchical importance and the crucial part they play in determining how situations of this kind turn out.

In addition to the standard feature importance rankings, Partial Dependence Plots (PDPs) were generated for the top variables-such as pedestrian age, vehicle types, and road features – to examine their marginal effect on injury severity predictions (Figure 5). For instance, PDPs showed that the probability of grievous injury increases significantly for pedestrians over 60 years of age and on narrow or curved roads. Similarly, crashes involving heavy vehicles like trucks and buses consistently showed a higher probability of severe injury outcomes. In contrast, two-wheelers and three-wheelers were associated with lower probabilities, typically below 60%. Cars and jeeps presented intermediate risk levels. Roads with curves or poor geometric alignment showed higher predicted injury severity, with PDPs indicating a 15-20% increase in the likelihood of grievous injury compared to straight roads; these findings reinforced the critical role of roadway geometry in pedestrian safety. The model also demonstrated that the likelihood of predicting grievous injury increased sharply when more than one person was injured in the crash, suggesting that multi-causality events are generally more severe.

While SHAP (Shapley Additive Explanations) offers detailed, instance-level insights by quantifying each feature’s contribution to a specific prediction, applying SHAP at scale was limited in this study due to the size and structure of the dataset. SHAP can be utilized in future extensions of the work to enhance interpretability and support policy recommendations at both the aggregate and case-specific levels.

To validate the robustness of the Random Forest Model, the study extended to include a comparative modelling with three other classification algorithms: Multinomial Logistics Regression (MLR), Support Vector Machine (SVM) with RBF kernel, and a standalone Decision Tree classifier. These models were selected as common baselines to evaluate performance across diverse algorithmic families-statistical, margin-based, and tree-based methods. Each model was trained on the same dataset and optimized using grid search. Performance was evaluated using a 5-fold stratified cross validation approach to ensure generalizability and fairness in comparison. The outcomes of this comparative analysis are presented in next section.

To evaluate the suitability of the Random Forest Classifier, a comparative analysis using three baseline models such as Multinomial Logistic Regression (MLR), Support Vector Machine (SVM) and Decision Tree classifier. Each model was trained on the same pre-proceeding dataset with 6104 entries and 16 features. The dataset was split into 75% training and 25% testing, and a 5-fold cross-validation strategy was adopted for validation. The hyper parameters were tuned using grid search to ensure fair comparison.

Table 6 presents the performance comparison of models where Random Forest achieved the highest classification performance across all metrics, followed by the Decision Tree and SVM models. Logistics Regression, although interpretable, performed the least well, likely due to its assumption of linear boundaries. These results affirm the robustness of Random Forest handling non-linear, high-dimensional crash data, justifying its selection for the primary predictive task in this study.