Generalized Sichel Crash Predictive Model: Analysis of Predictor-Dependent Overdispersion in Urban Signalized Intersections
DOI: 10.21203/rs.3.rs-5719474/v1
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Summary
This study addresses the limitations of traditional crash prediction models, specifically the Negative Binomial (NB) distribution, in handling overdispersed and long-tailed crash data at urban signalized intersections. While NB models are widely used, they often fail to accurately estimate dispersion levels in such data. The authors propose the Sichel (SI) distribution, a combination of Poisson and inverse Gaussian distributions, as a more flexible alternative. The research aims to compare NB and SI models under both fixed and predictor-dependent dispersion states to determine which better predicts crash frequencies and estimates dispersion parameters. The analysis utilized geometric, traffic, and crash data from 41 signalized intersections in Qazvin, Iran, covering the years 2014–2016. Predictor variables included annual crash counts, average daily traffic volume (AADT), intersection length, and lane width. The researchers developed simple models with constant dispersion parameters and generalized models where dispersion depended on intersection length. They also evaluated reduced models by removing non-significant variables. Statistical modeling and hypothesis testing were conducted using R programming libraries. Results indicated that crash data were significantly overdispersed, rendering Poisson models unsuitable. In simple modeling, the SI model outperformed the NB model based on goodness-of-fit criteria (AIC and BIC). However, in the simple SI model, lane width was not statistically significant, leading to a reduced model that performed best among simple variants. In generalized modeling, the full Generalized Sichel (GSI) model demonstrated superior efficiency compared to the Generalized Negative Binomial (GNB) model, with lower -LogLikelihood (180.03 vs. 183.36), AIC (368.06 vs. 374.73), and BIC (375.78 vs. 383.45). The generalized models revealed that intersection length significantly influenced dispersion, and lane width had a significant inverse relationship with crash frequency in the full GSI model. Traffic volume showed a positive correlation with crashes in all models. The study concludes that the full generalized Sichel model provides a more accurate and efficient prediction of crash frequencies than the generalized Negative Binomial model for urban signalized intersections. The SI model’s ability to handle predictor-dependent overdispersion allows for more precise estimation of dispersion levels and better identification of the effects of geometric factors like lane width. These findings suggest that the Sichel distribution is a robust alternative to traditional NB models for analyzing overdispersed crash data with long tails, offering improved reliability for safety planning and countermeasure development.
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| Stage | Outcome | Tool | Model | Prompt | Attempts | Completed |
|---|---|---|---|---|---|---|
| discover | success | Crossref | — | — | 1 | 2026-06-25 |
| archive | success | canonical_url | — | — | 1 | 2026-06-26 |
| extract | success | cached | — | — | 2 | 2026-06-26 |
| clean | success | clean | — | — | 1 | 2026-06-25 |
| chunk | success | chunk | — | — | 1 | 2026-06-25 |
| embed | success | embed | Qwen/Qwen3-Embedding-8B | — | 1 | 2026-06-25 |
| promote | success | — | — | — | 1 | 2026-06-25 |
| summarize | success | llm | qwen3.6-27b-prismaquant | summ-v5 | 1 | 2026-06-26 |
| tag | success | vector_similarity | — | — | 6 | 2026-06-25 |
| verify | success | — | — | — | 1 | 2026-06-26 |
Summary generated by qwen3.6-27b-prismaquant on 2026-06-26; verification: verified.
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- Empirical Findings: crash risk outcomes