Examination of Crash Variances Estimated by Poisson–Gamma and Conway–Maxwell–Poisson Models
Bibliographic record
Abstract
The Poisson–gamma (negative binomial or NB) distribution is still the most common probabilistic distribution used by transportation safety analysts to model motor vehicle crashes. Recent studies have shown that the Conway–Maxwell–Poisson (COM–Poisson) distribution also is promising for developing crash prediction models. The objectives of this study were to investigate and compare the estimation of crash variance predicted by the COM–Poisson generalized linear model (GLM) and the traditional NB model. The comparison analysis was carried out with the most commonly employed functional forms, which linked crashes to the entering flows and other explanatory variables at intersections or on segments. To accomplish the objectives of the study, several NB and COM–Poisson GLMs (including flow-only models and models with several covariates) were developed and compared by using two data sets. The first data set contained crash data collected at signalized, four-legged intersections in Toronto, Ontario, Canada. The second data set included data collected on rural, four-lane, undivided highways in Texas. The results of this study show that the trend of crash variance prediction by COM–Poisson GLM is similar to that predicted by the NB model. The Spearman's rank correlation coefficients between the crash variance predicted by the COM–Poisson and the NB model confirmed that there was a perfect monotone increasing, and the values were highly correlated. This correlation means that a site characterized by a large variance would essentially be identified as such, whether the NB model or the COM–Poisson model was used.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.020 | 0.064 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".