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REPRODUCIBLE STUDY 01 · LONDON · EXPLORATORY
A London-specific baseline improves the fit. Qualifications alone do not yet provide a consistently supported extra signal. Inspect the evidence, change the mileage assumptions, and rerun the complete study.
RESULT · EVIDENCE · COMPARATOR
| Candidate | Comparator | Gain | 95% refit range | Observed / expected |
|---|---|---|---|---|
| Selected London baseline | National baseline | +53.46% | +3.16% to +73.09% | 1.006 |
| Qualifications · continuous | Selected London baseline | -3.41% | -14.61% to +7.72% | 1.015 |
| Qualifications · bands | Selected London baseline | +4.18% | -9.97% to +24.35% | 1.003 |
| Combined social · continuous | Selected London baseline | +14.23% | -8.67% to +26.14% | 1.003 |
| Candidate | 2025 borough holdout | Without City & Westminster, refitted |
|---|---|---|
| Selected London baseline | +54.24% | +11.38% |
| Qualifications · continuous | -5.65% | -5.96% |
| Qualifications · bands | +0.88% | -2.39% |
| Combined social · continuous | +17.94% | +5.23% |
City of London and Westminster remain in the main study. Removing them triggers full reselection and materially reduces the pooled regional-baseline gain. Borough holdout removes each authority’s outcomes from training; its available lagged history remains a predictor. These are exploratory diagnostics.
PHASE TWO · ROBUSTNESS & VALIDATION
Read direction, effect size and uncertainty separately. A positive score under every tested assumption is evidence of directional consistency, not proof of future performance.
| Candidate | Positive years | Mileage gain range | Borough holdout | Without central pair | 95% refit range | Direction |
|---|---|---|---|---|---|---|
| Selected regional baseline | 3/3 | +47.65% to +59.19% | +54.24% | +11.38% | +3.16% to +73.09% | Positive across these checks |
| Qualifications — continuous | 0/3 | -3.41% to -3.28% | -5.65% | -5.96% | -14.61% to +7.72% | Negative across these checks |
| Deprivation — continuous | 3/3 | +3.90% to +11.02% | +12.58% | +4.06% | -11.85% to +24.96% | Positive across these checks |
| Combined — continuous | 3/3 | +8.47% to +19.52% | +17.94% | +5.23% | -8.67% to +26.14% | Positive across these checks |
| Qualifications — bands | 3/3 | +2.82% to +5.05% | +0.88% | -2.39% | -9.97% to +24.35% | Direction changes across checks |
| Deprivation — bands | 3/3 | +4.62% to +5.82% | -8.77% | +7.45% | -3.95% to +30.65% | Direction changes across checks |
| Combined — bands | 3/3 | +5.83% to +8.37% | -16.71% | +2.39% | -7.65% to +35.63% | Direction changes across checks |
The selected regional baseline is compared with the national model. Social candidates are compared with that selected regional baseline. Mileage ranges cover five refitted point scenarios; they are not confidence intervals. Borough holdout covers 2025; central-pair exclusion covers 2023–2025. Different diagnostic populations are never combined into one score.
| Model | Comparator | Rows | Poisson deviance ↓ | Gain ↑ | O/E (target 1) | Weighted absolute rate error ↓ |
|---|---|---|---|---|---|---|
| National baseline | Reference | 99 | 2,225.11 | — | 0.920 | 0.01586 |
| London coefficients; national history prior | N | 99 | 1,563.51 | +29.73% | 1.030 | 0.01304 |
| Selected partial pooling; national history prior | N | 99 | 1,570.61 | +29.41% | 0.977 | 0.01304 |
| V1 selection; national history prior | N | 99 | 1,614.19 | +27.46% | 0.961 | 0.01330 |
| Complete London baseline + Inner/Outer | N | 99 | 1,035.57 | +53.46% | 1.006 | 0.01050 |
| Selected regional baseline | N | 99 | 1,035.57 | +53.46% | 1.006 | 0.01050 |
| Previous local baseline (no Inner/Outer) | N | 99 | 1,031.98 | +53.62% | 1.006 | 0.01047 |
| Qualifications — continuous | S | 99 | 1,070.86 | -3.41% | 1.015 | 0.01076 |
| Deprivation — continuous | S | 99 | 958.56 | +7.44% | 1.001 | 0.01021 |
| Combined — continuous | S | 99 | 888.15 | +14.23% | 1.003 | 0.00993 |
| Qualifications — bands | S | 99 | 992.33 | +4.18% | 1.003 | 0.01048 |
| Deprivation — bands | S | 99 | 980.10 | +5.36% | 1.001 | 0.01024 |
| Combined — bands | S | 99 | 960.24 | +7.27% | 1.000 | 0.01028 |
Absolute rate error is exposure-weighted, in collisions per 100,000 motor miles. Poisson deviance scores the NB2 predictions; it is not an NB2 likelihood. Baselines remain visible even when their scores coincide.
These are the original London-wide protocol gates, unchanged by the geography selector. The direction summary above is descriptive and adds no new pass threshold.
| Candidate | Passed | Failed | Recorded decision |
|---|---|---|---|
| Selected regional baseline | Pooled gain ≥1%; Every annual gain ≥1%; 95% refit lower bound >0; Borough holdout gain >0; Calibration within 10%; Absolute rate error no worse | None of these gates | Exploratory baseline candidate; pricing not approved |
| Qualifications — continuous | Calibration within 10%; Support and full rank | Pooled gain ≥1%; Every annual gain ≥1%; 95% refit lower bound >0; Borough holdout gain >0; Absolute rate error no worse | Not consistently supported; pricing not approved |
| Deprivation — continuous | Pooled gain ≥1%; Borough holdout gain >0; Calibration within 10%; Absolute rate error no worse; Support and full rank | Every annual gain ≥1%; 95% refit lower bound >0 | Not consistently supported; pricing not approved |
| Combined — continuous | Pooled gain ≥1%; Every annual gain ≥1%; Borough holdout gain >0; Calibration within 10%; Absolute rate error no worse; Support and full rank | 95% refit lower bound >0 | Not consistently supported; pricing not approved |
| Qualifications — bands | Pooled gain ≥1%; Every annual gain ≥1%; Borough holdout gain >0; Calibration within 10%; Absolute rate error no worse | 95% refit lower bound >0; Support and full rank | Not consistently supported; pricing not approved |
| Deprivation — bands | Pooled gain ≥1%; Every annual gain ≥1%; Calibration within 10%; Absolute rate error no worse | 95% refit lower bound >0; Borough holdout gain >0; Support and full rank | Not consistently supported; pricing not approved |
| Combined — bands | Pooled gain ≥1%; Every annual gain ≥1%; Calibration within 10%; Absolute rate error no worse | 95% refit lower bound >0; Borough holdout gain >0; Support and full rank | Not consistently supported; pricing not approved |
STRESS THE DENOMINATOR
Each scenario refits the national anchor, training-only baseline selection and social models. London’s current and lagged mileage change together. These ±20% stresses are assumptions, not estimated error bars.
The published DfT exposure is the reference. Collision counts, social inputs and assessment rows stay fixed.
| Candidate | Comparator | Reference gain | Scenario gain |
|---|---|---|---|
| Selected London baseline | National baseline | +53.46% | +53.46% |
| Qualifications · continuous | Selected London baseline | -3.41% | -3.41% |
| Qualifications · bands | Selected London baseline | +4.18% | +4.18% |
| Combined social · continuous | Selected London baseline | +14.23% | +14.23% |
The scenarios test robustness; they do not select a new preferred exposure estimate. No new scenario confidence intervals or pricing approval are implied. This authority-level exercise is separate from the LSOA mileage pilot.
REPRODUCE THE REFERENCE RESULTS
The ZIP contains the frozen 1,064-row authority panel, original model code, reference outputs, pinned dependencies, study specification, data dictionary, assumptions and separate calculation checks. The analysis runs offline after installing its dependencies.
python3 -m venv .venv
.venv/bin/python -m pip install -r requirements.txt.venv/bin/python reproduce.py --full-bootstrap.venv\Scripts\python.exe. The README includes both platform instructions.All 2,925 temporal, borough-holdout and central-pair prediction values matched exactly. All 399 bootstrap draws were freshly rerun; the same four failed draws were retained and the interval summaries matched. Five mileage scenarios passed another 705 independent arithmetic and reconciliation checks.
This rerun starts at the frozen model-input snapshot. It does not rebuild that snapshot from raw publisher files. Source archives and preparation lineage are identified for inspection.
python3 reproduce.py --audit-only checks saved files and arithmetic using the standard library. It does not fit models. Running reproduce.py without flags refits the point estimates and mileage scenarios, but reconstructs bootstrap intervals from archived draws. Use --full-bootstrap for fresh bootstrap fits.
The arithmetic checker uses a separate code path and imports no model implementation. It is an automated calculation review, not an independent human actuarial review. Numerical agreement does not resolve selection bias, omitted controls, old Census context or pricing suitability.
Download the actual validation record · JSONTHE STUDY CONTRACT
| Type | Item | Assumption |
|---|---|---|
| Observed | Collision numerator | Published injury-collision counts, road location. Damage-only incidents and insurance claim costs are absent. |
| Estimated | Mileage denominator | DfT estimated all-motor vehicle miles, joined by authority and year. Realised target-year exposure is used for assessment; this is not an at-origin mileage forecast. |
| Constant | Census context | 2011 age, density and qualification shares are held fixed through 2018–2025. They describe residents around roads, not drivers. |
| Observed | Historical deprivation | Use 2015/2019 published income and employment scores by recorded availability. No 2025 deprivation or 2021 education backdating. |
| Allocated | Mileage stress scenarios only | Inner/Outer reweighting is a hypothetical authority-level allocation; two scenarios preserve annual London totals. No LSOA mileage is allocated in the main study. |
| Estimated | Model and selection | NB2 fits, training-only history prior and transformations. The 1% deviance selection tolerance favours stronger pooling. Models and gates are retained unchanged. |
| Constant | Frozen cohort and folds | 133 complete-history English authorities; 33 London boroughs assessed. 2020/2021 are excluded as training outcomes but can appear as lagged predictors. Cohort inclusion uses retrospective data availability. |
| Constant | Uncertainty design | 399 authority-history bootstrap draws; four failures retained, 395 complete. Marginal percentile ranges omit residual spatial dependence and multiplicity adjustment. |
Of 399 authority-history bootstrap draws, 395 completed. Draws 4, 7, 9 and 102 failed and were not replaced. The marginal 95% refit ranges omit neighbouring-borough dependence and multiplicity adjustment. Annual assessment windows overlap.
The original V2 candidate set was amended after inspecting V1 point results. Nested selection protects each fit from direct assessment-year tuning; it cannot make these outcomes fresh validation. Qualification bands lack minimum authority support in D9. Income and employment are strongly correlated.
Historical road-class × urban/rural exposure remains incomplete. The frozen complete-history cohort uses retrospective availability. No LSOA mileage allocation, individual-driver education effect, causal explanation or production risk multiplier is established here.
| Field | Unit | Meaning |
|---|---|---|
id | text | Unique authority code:year key |
areaId | ONS authority code | Exact code; no approximate boundary backcast |
name | text | Authority name for display |
region | text | English region; London is target geography |
year | calendar year | Outcome and realised exposure year |
collisions | event count | Police-reported personal-injury collisions at road location; includes non-motor-only events; not insurance claims |
motorMiles | motor vehicle miles | DfT all-motor, all-road annual authority exposure; no population allocation |
incomeScore | fraction | Published income domain average score, historical vintage |
employmentScore | fraction | Published employment domain average score, historical vintage |
deprivationVintage | release year | 2015 or 2019 edition available before forecast origin |
deprivationPublished | ISO date | Publication date of deprivation edition |
lagYear | calendar year | Outcome year minus two |
lagCollisions | event count | Same-authority personal-injury collisions two years earlier |
lagMotorMiles | motor vehicle miles | Same-authority exposure two years earlier |
lagCarTaxiShare | fraction | Cars/taxis miles divided by all-motor miles at lagYear |
lagLogMilesPerRoadKm | natural log | Log of lagged motor miles / road length in kilometres |
population2011 | residents | Fixed Census 2011 population; not exposure |
populationDensity2011 | residents per km² | 2011 population / (published hectares / 100) |
ageUnder25Share2011 | fraction | Residents under 25 / own Census age-table population |
age65PlusShare2011 | fraction | Residents 65+ / own Census age-table population |
noQualificationsShare2011 | fraction | 2011 residents aged 16+ with no qualifications / residents aged 16+; not driver education |
level4PlusShare2011 | fraction | 2011 residents aged 16+ with Level 4+ qualifications; retained but not the education feature fitted here |
logDensity2011 | natural log | Log of 2011 population density |
SOURCES & REUSE
Open Government Licence v3.0; retain publisher attribution and check source-specific exceptions.
Open Government Licence v3.0; retain publisher attribution and check source-specific exceptions.
Open Government Licence v3.0; retain publisher attribution and check source-specific exceptions.
Open Government Licence v3.0; retain publisher attribution and check source-specific exceptions.
Open Government Licence v3.0; retain publisher attribution and check source-specific exceptions.
Open Government Licence v3.0; retain publisher attribution and check source-specific exceptions.
Open Government Licence v3.0; retain publisher attribution and check source-specific exceptions.
Publisher terms; the pack retains the 33-code classification and citation, not the report.
The source manifest names exact source vintages, original-byte hashes and archived downloads. The frozen input snapshot is 10 October 2026; no current publisher file is silently substituted.
Suggested citation: Johan Strydom (2026), London regional baseline and qualifications: reproducible study v1. Analytical snapshot 10 October 2026; reproduction release 20 October 2026. Study ID: london-qualifications-reproducible-v1.