Dear Seyedehsan Dadvar To me, including both secondary and primary crashes in one specific statistical model does not make sense since the crash mechanisms are different. Although both of the cases deal with traffic characteristics within crash precursors, the secondary crashes are under the impact of primary crashes within limited distance and time duration. Indeed, for Real-Time Risk Assessment (RTRA) of primary crashes, we monitor and track the traffic turbulence that is changing due to the nature of traffic characteristics during a specific time window. However, in the case of secondary crashes, traffic turbulence is mainly due to the primary crashes not the nature of traffic characteristics.

Therefore, not only the analysis would be different, but also the data collection process is different where you need to consider only those cases that have at least two consecutive crashes within a short period of time (maybe about 30 minutes) and short distances. I also suggest you read the following paper that includes a comprehensive literature review in RTRA:

“Real-time crash prediction models: State-of-the-art, design pathways and ubiquitous requirements”

Thank you Arash Khoda Bakhshi for thoughtful response and shared article.

But the point is that I did not limit the modeling procedure to a single model including both primary and secondary crashes. There can be multiple models similar to the structure of the HSM (e.g., different components for crash prediction such as collision type and crash severity: single-vehicle, multiple-vehicle, and driveway-related, FI vs PDO, and other disaggregations due to the nature of data and better fit). There are cases that the prevalence of secondary crashes seem to be linked to the inability to evacuate primary crashes (e.g., narrow sized shoulders that may aggravate secondary crashes upon lane closure due to primary crash); therefore, comprehensive analysis of primary and secondary crashes while controlling for differences and data collection approaches would improve the overall crash predictability.

Seyedehsan Dadvar,

I totally agree with your opinion. Definitely, crash occurrences change traffic patterns. As you mentioned, inability is evacuating traffic congestion resulted from primary crashes increase the probability of secondary. Moreover, even if we evacuate primary crashes properly, we will still have a significant unpredictable reduction in speed mean at downstream and increase in speed variation compared to upstream that are crucial in secondary crash happening. By the way, I refer you to this paragraph copied from “The Statistical Analysis of Crash-Frequency Data: A Review and Assessment of Methodological Alternatives” by Lord and Mannering that will shed a light on your research:

“The most common duration-model approach is a hazard-based model that considers the conditional the probability of a crash happening at some time t +dt given that it has been time t since the last crash occurred. Hazard-based models can be estimated under a wide variety of distributional assumptions and non-parametric forms and allow important inferences to be made on how the probabilities of having a crash change over time.”

Thank you Arash Khoda Bakhshi for expanding the discussion and excerpt from paper by Lord and Mannering. I have to re-review that paper!