Modelling Approach

Three models, in sequence

The project produces a single output — a risk score per road link per year — but it does so via three models chained together. Each addresses a different gap in the available data, and each stage feeds the next.

Stage What it predicts Why it exists Output
1a — Traffic volume AADT for every road link DfT measures traffic at ~13,000 count points; the network has 2.1M links aadt_estimates.parquet
1b — Time-zone profiles Within-day traffic shape (peak / pre-peak / off-peak fractions) WebTRIS sensors are sparse; profiles let temporal exposure be projected to all links timezone_profiles.parquet
2 — Collision risk Expected collisions per link per year The headline risk model — uses Stage 1a output as exposure risk_scores.parquet

Each stage has its own page documenting the data, features, validation, and known limitations. This page is an orientation: how the three fit together and why the project needs all three.

Why exposure has to be modelled, not measured

Comparing collision counts across roads requires a denominator. A motorway with 100,000 vehicles per day should have more collisions than a country lane with 500 — that’s not a safety problem, it’s a volume problem.

The natural denominator is AADT (Annual Average Daily Flow), and DfT publishes AADF for ~13,000 count points across the study area. But the project scores 2.1 million road links. Most of the network — particularly minor and unclassified roads where collision under-counting is most severe — has no nearby count point.

Stage 1a trains a gradient-boosted model on the directly counted AADF rows, learning the relationship between road class, location, network position, and traffic volume. It then applies that relationship to every link in the network, producing an AADT estimate for the 99.4% of links without a count point.

The CV R² of ~0.83 (counted-only training set) means the estimator captures the dominant patterns but is not perfect — uncertainty in AADT is propagated forward and shows up in the residual structure of Stage 2.

→ Stage 1a: Traffic Volume

Why temporal profiles are a separate model

Time-of-day matters for risk: an empty motorway at 3am is a different exposure regime to the same road in rush hour. WebTRIS sensors on the National Highways network record sub-daily flow profiles (peak vs off-peak fractions), but they exist only on motorways and trunk A-roads — a tiny fraction of the full network.

Stage 1b treats the WebTRIS profiles as training data and learns to predict the within-day shape from features the rest of the network shares with it (road class, AADT, network position). The output is a peak / pre-peak / off-peak fraction triple per link.

These profiles are currently produced as a separate output for downstream temporal analysis. They are not part of the Stage 2 collision feature set — see Future Work for plans to integrate them.

→ Stage 1b: Time-Zone Profiles

The risk model itself

Stage 2 is the model the project exists to produce. It predicts annual collision counts per road link, using Stage 1a’s AADT estimates as an exposure offset:

log(expected collisions) = log(AADT × length_km × 365 / 1e6) + β·X

The offset term means the model learns which roads are dangerous given their traffic, not just which roads are busy. A short minor road with three collisions and 500 vehicles per day comes out as higher-risk than a long motorway link with three collisions and 100,000 vehicles per day.

Two model classes are fit on the same data:

  • A Poisson GLM for interpretable coefficients (incidence rate ratios) and residual diagnostics. Used to identify “excess risk” links where observed counts substantially exceed the model’s prediction.
  • An XGBoost model for the headline risk percentile. Captures the non-linear interactions a GLM misses, at the cost of being harder to interpret directly. SHAP values fill that gap.

The XGBoost output drives risk_percentile. The GLM provides the diagnostic residuals.

→ Modelling page (Stage 2 detail)

Decisions that span all three stages

A few choices apply across the pipeline rather than to any single model:

Group-aware cross-validation. Stage 1a uses GroupKFold by count_point_id, Stage 1b by site_id, and Stage 2 uses GroupShuffleSplit by link_id. This prevents leakage where a model sees the same physical road at training and test time and inflates its apparent performance.

Forbidden post-event columns. Several columns in the joined data are derived from collision records themselves (e.g. pct_dark, pct_urban, mean speed at collision sites). These are excluded from modelling features by an explicit guard in model/collision.py — see Engineering Conventions for detail. Using them would mean the model “predicts” collisions partly by looking at the collisions it’s trying to predict.

Validation across stages

Each stage has its own held-out validation:

  • Stage 1a: CV R² ~0.83 on counted-only AADF rows.
  • Stage 1b: CV R² ~0.65 on core_daytime_frac, ~0.46 on late_evening_frac (weakest band).
  • Stage 2: Out-of-sample pseudo-R² about 0.32 for the post-fix XGBoost baseline (five-seed mean 0.323, with temporal features included), and 0.347 for the GLM in-sample on the downsampled training set.

The Stage 1a and Stage 2 metrics are not directly comparable — different targets, different null models, different row subsets. See Model Inventory for full performance metrics and Empirical Bayes Shrinkage for the post-modelling adjustment that handles overconfidence on zero-collision links.

Earlier internal docs and site pages cited a Stage 2 XGBoost pseudo-R² around 0.86. That number came from a pre-fix evaluation surface that was later superseded after a Stage 2 feature-table bug and leakage issue were diagnosed. For current project positioning, use the post-fix ~0.32 baseline instead.

What this section covers