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Persistence and validation · Phase 8
Test the frozen frost model in another year and different places. Inspect annual tail comparisons alongside conditional LSOA and counted-road evidence.
The frozen authority model improves 2025 deviance by 10.35%, but calibration and geographical consistency miss the declared targets. Only two of five final-year geographical folds improve. A1–A10 remain unchanged. LSOA mileage estimates are conditional, and the pilot has no 2025 exposure panel.
Definitions, eligibility, fixed bands, time splits and later decision thresholds are recorded before frost–outcome analysis.
Read the protocol ↓33,505 LSOAs have usable road-weighted scores. A separate area-weighted sensitivity retains its own cutpoints.
Inspect the features ↓The authority panel and original LSOA inventory are built. A later pilot adds conditional LSOA miles; independent denominator validation remains open.
Inspect the remaining gates ↓Rates, exposure, uncertainty and regional comparisons are available for authorities. The full LSOA and major-road gates remain open.
Explore descriptive results ↓A development-selected baseline is frozen and assessed on 2024. Review London first, then South East, with calibration, overdispersion and geographical checks.
Review the baseline ↓Review the frozen candidate, matched model comparison, adjusted effects and frost/ice diagnostics. The annual-weather test and scientific validation gates remain open.
Review the incremental test ↓Compare major-road allocation, minor-road flow predictions and frost-related stress scenarios across London, South East and South West.
Inspect exposure assumptions ↓No merge establishes practical equivalence. Inspect the nested selection audit and the original A1–A10 mapping frozen for phase 8.
Review band-selection evidence ↓Review the frozen 2025 assessment, regional and spatial tests, annual tail contrasts and stricter counted-road subset. Phase 9 remains the final evidence consolidation.
Review persistence results ↓Met Office HadUK-Grid v1.1.0.0 provides the 1991–2020 annual air-frost normal. The newer 1 km CEDA files require sign-in and have not been loaded. The road weights use the April 2026 OS Open Roads snapshot, so this is a retrospective geographical study.
PHASE 8 · YEAR AND GEOGRAPHICAL PERSISTENCE
The primary assessment keeps phase 7’s coefficients and authority bands frozen. It predicts 2025 using 2023 controls and calendar effects, with realised official motor miles as exposure. These data were previously inspected descriptively: this is retrospective validation.
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PHASE 7 · ADJACENT-BAND SIMPLIFICATION
The rule is deliberately practical: adjusted rate ratios must be supported within 0.95–1.05, and simplification may lose at most 0.1% of development validation performance. Whole authorities and their repeated years stay together in geographical folds.
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LSOA MILEAGE PILOT · 2021–2024
London, South East and South West provide urban, mixed and rural contrasts. Published major-road traffic is allocated to road alignments where matching succeeds. The remaining authority mileage is allocated across minor roads using estimated flow and mapped length.
These estimates support sensitivity analysis. No LSOA has passed independent allocation validation. Reconciliation to authority totals does not establish how accurately miles are distributed between neighbourhoods. Travel through an LSOA is different from mileage driven by its residents.
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PHASE 6 · INCREMENTAL PREDICTION
Six candidates use the same authorities, collision counts and motor miles. The model choice is made with 2021–2023 data; 2024 assesses the frozen choice. Authority bands A1–A10 remain distinct from the LSOA deciles.
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PHASE 5 · REGIONAL BASELINES
The baseline accounts for regional, settlement and traffic differences using the matched authority panel. It contains no frost score or decile. London is reviewed first, then South East and the remaining English regions.
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PHASE 4 · DESCRIPTIVE EVIDENCE
Compare rates on the roads for which matched exposure is available: all roads within eligible highway authorities. A1–A10 rank authority frost means. The original LSOA deciles remain D1–D10 and have no validated local-mileage denominator.
Raw rates can reflect density, region, road mix and reporting. They do not establish that frost increases or reduces risk, or that it improves a prediction model. Major-road-only frequency, LSOA frequency, elevation and detailed road-class composition remain unavailable.
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PHASE 2 · FIXED GEOGRAPHICAL FEATURE
D1 has the fewest frost days; D10 has the most. Every eligible LSOA has equal weight when the national cutpoints are set. Changing region filters the distribution of bands; it does not recalculate them.
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PHASE 3 · NUMERATOR AND DENOMINATOR
The primary outcome counts each police-reported injury collision once when at least one vehicle belongs to a declared motor category covered by the traffic denominator. Unknown vehicle types and collisions involving only out-of-scope vehicles remain separate.
Exact-code annual motor miles, the corrected collision numerator and authority-scale frost context are joined. The balanced cohort contains 131 authorities.
Phase 4 uses this panel for descriptive authority screening. It cannot establish an LSOA decile effect.
465,246 motor-involved collisions have a unique English LSOA assignment. The inventory retains 39,606 rows with no assigned collision.
This original v1 inventory has no LSOA mileage. The separate mileage pilot above adds modelled exposure; independent validation for unsampled roads remains open.
All five DfT geometry files use two-point endpoint chords. Matching count-point identifiers does not establish the road path through each LSOA.
The exposure catalogue preserves flows, length and Counted / Estimated flags. The later mileage pilot above supplies a restricted centreline-matched subset and its audit; it does not validate the complete major-road catalogue.
| Year / role | English-authority motor collisions | Located in an English LSOA | English-authority collisions unassigned | Eligible authority rows | English major-road links |
|---|---|---|---|---|---|
| 2021Development | 91,890 | 91,483 | 407 | 138 | 14,475 |
| 2022Development | 96,592 | 96,249 | 343 | 131 | 14,403 |
| 2023Development | 94,848 | 94,461 | 387 | 133 | 14,404 |
| 2024Validation | 91,733 | 91,357 | 376 | 140 | 14,473 |
| 2025Descriptively inspected | 92,015 | 91,696 | 319 | 140 | 14,476 |
1,832 motor-involved collisions with an English highway-authority code could not be assigned uniquely. Another 152,591 located motor collisions lie within 10 m of an LSOA border. The LSOA inventory reports assigned events; complete local counts have not been established for all areas.
| Check | State | Evidence |
|---|---|---|
| Frozen source hashes and collision joins | Passed | 513,801 collision IDs and 937,265 vehicle records; no duplicate keys, orphans or declared-vehicle count mismatches. |
| Full LSOA boundary and feature population | Passed | 33,755 unique English LSOA2021 areas; full polygon components checked against the original ZIP. |
| Compact-weight replay | Passed | Every numerical frost feature and both fixed cutpoint sets replay from the saved weights. |
| Source-to-spatial collision reconciliation | Passed | Assigned, ambiguous and outside-polygon motor events reconcile to the English-authority source universe. |
| Exact highway-authority geography | Open | Barnsley and Sheffield had a 2025 boundary change. Original UTLA23 LSOA memberships remain intact; an automatic bridge to the current authority rates is withheld. |
| Historical major-road path allocation | Open | All annual MRDB links have only two points. Physical route geometry and event-to-link assignments have not passed. |
| Independently validated all-road LSOA miles | Open | Unsampled minor-road traffic and exposure uncertainty are unresolved; every LSOA frequency remains null. |
PHASE 1 · FROZEN SPECIFICATION
The later question is whether frost deciles improve collision-frequency predictions after accounting for traffic exposure and area characteristics. A geographical gradient alone will not meet that test.
| Outcome and units | Distinct eligible injury collisions ÷ matched motor-vehicle miles × 100,000. Positive-exposure rows with zero collisions remain in the panel. |
|---|---|
| Climate feature | Fixed 1991–2020 mean annual air-frost days. Road-length weighting is primary; land-area weighting is a separately versioned sensitivity. Air frost is a climate indicator, not road-surface ice. |
| National bands | Nine empirical inverse-CDF cutpoints, equal eligible-LSOA weights. Ties share a band; the lower interval includes its upper boundary. Cutpoints stay fixed across every year and region. |
| Development and assessment | Develop on 2021–2023, validate on 2024, and retain 2025 for assessment under the frozen model rules. Phase 4 now displays 2025 frost associations descriptively; it is no longer untouched. Repeat development without 2021 and use a new untouched year for prospective confirmation. |
| Geographical assessment | Five folds containing whole authorities or contiguous areas; shared underlying road links stay together. Random LSOA splitting is excluded. |
| Later model comparison | Use count models with a log-mileage offset. Compare a baseline, continuous frost and fixed deciles on the same assessment rows. Account for rurality, road and traffic mix, geography and year. |
| Later promotion threshold | At least 0.5% lower final-assessment Poisson deviance, positive improvement in 2024 and at least four spatial folds, plus a spatial-bootstrap 95% interval above zero. These are predeclared study choices, not findings. |
| Claim boundary | Police-reported injury collisions. This study does not measure damage-only accidents, insurance claims, fault or a causal effect of frost. |
The road score is the sum of each grid cell’s frost normal multiplied by the mapped road length inside that cell and LSOA, divided by the covered mapped road length. Area weighting uses intersected square metres instead.
OS road identifiers are deduplicated. A road portion coincident with a shared LSOA border is assigned once using the lowest LSOA code. No collision count enters the weights or cutpoints. Missing grid coverage is retained as a quality flag; it does not become zero frost.
Mapped private or restricted roads can contribute to the static climate feature. The April 2026 road snapshot is not substituted for historical 2021–2025 traffic exposure. The full construction and source hashes are in the downloads.
TRACEABLE INPUTS AND OUTPUTS
HadUK-Grid v1.1.0.0, public Climate Data Portal product at 2 km. All 63,296 published grid cells retrieved and checked; no annual 2021–2025 weather anomalies are included.
England and Wales BFC V10 polygons, clipped to mean high water. The study keeps all 33,755 English areas and checks actual extracted source bytes.
April 2026 generalised road alignments provide static frost weights. Fictitious links are excluded. The snapshot does not supply historical traffic or establish complete public-road mileage.
Frozen 2021–2025 final collision, vehicle and coding-guide archives. Motor eligibility is explicit; each collision counts once. The September 2026 powered-transporter coding is handled.
Exact authority-year all-motor miles and 2021–2025 major-road files. Counted / Estimated flags are retained; endpoint-chord geometry is rejected for LSOA mileage allocation.
Link and small-area estimates carry more uncertainty. Authority agreement alone cannot validate the distribution of traffic within an authority.