## 4 Experimental Results
### Addressing RQ2: Impact of PR Behaviors on Contributor Engagement in GitHub Projects
#### 4.3.2 Probability of Immediate PR Processing and Average Time Step to Process PR  
This section explores the influence of the immediate processing probability of PRs and the average time until PRs are processed, using SHAP values derived from the model. Figure 9 shows the results of the SHAP values of the independent variables related to PR handling. Figure 9a illustrates the impact of the probability of immediate PR processing (x_processing) on participant activity duration. The analysis reveals that when the probability of immediate processing is close to 0, SHAP values are negative, indicating a detrimental effect on activity duration. Conversely, as the probability approaches 1, SHAP values shift positively, suggesting that prompt responses to PRs can enhance participant engagement. Figure 9: SHAP Analysis of x_processing and pr_to_processing. This highlights the importance of timely feedback in fostering sustained participation, particularly for participants located on the periphery of the network. Peripheral participants appear to be more significantly influenced by immediate PR processing, indicating that prompt handling of their PRs can encourage long-term activity. On the other hand, participants with high k-values--those in the network's core--are predominantly distributed around a 25% probability of immediate processing. This distribution suggests that these central participants are less affected by immediate processing, possibly due to their established roles and deeper integration within the project. Figure 9b examines the relationship between the average time taken to process PRs (pr_to_processing) and participant activity duration. While the data points in the graph are widely dispersed, making it challenging to discern a direct relationship, further interpretation using k-values reveals meaningful patterns. Participants located at the network's core (those with high k-values) tend to exhibit positive SHAP values when PR processing times are close to 0, indicating that quicker processing positively impacts their activity duration. Conversely, as processing times increase, SHAP values trend negatively, highlighting the potential for delays to discourage sustained activity. This finding suggests that efficient PR handling is particularly crucial for maintaining the engagement of central participants, who often play critical roles in project sustainability. Together, these results provide important insights into the role of PR management in shaping long-term participant activity. Immediate processing has a disproportionately positive effect on peripheral participants, helping to integrate them more effectively into the project. Meanwhile, reducing delays in PR handling ensures that core participants remain active and engaged. These findings emphasize the value of optimizing PR workflows to foster both peripheral and central participants' long-term participation, ultimately strengthening the overall health and sustainability of the project. 3.3 Average Time Between Branch Creation and PR Submission, and from PR Submission to New Branch Creation  
This section analyzes the time intervals between key actions related to PRs: the time from branch creation to PR submission (create_to_pr) and the time from PR submission to the creation of a new branch (pr_to_create). These intervals provide insights into how efficiently participants work within the project and how quickly they engage in subsequent activities, which could impact their long-term participation. Figure 10 shows the SHAP values results of the independent variables related to the relationship between branch creation and PR. Figure 10: SHAP Analysis of create_to_pr and pr_to_create. Figure 10a presents the SHAP dependence plot for the variable create_to_pr, which represents the time taken between creating a branch and submitting a PR. The analysis shows somewhat of a negative correlation between longer times to submit a PR and contributor participation duration.