Social factors and injury collision frequency — exploratory v2
Study: social-exploratory-2026-10-10-v2
Amended and fitted: 10 October 2026

PURPOSE AND STATUS
Test incremental prediction of police-reported personal-injury collision counts per matched motor-vehicle mile. This is retrospective area-level research, separate from the immutable original protocol v1 and its H1–H6 hypotheses. It does not estimate all accidents, insurance claims, fault, resident-driver risk or causation. No human actuarial review or approved analytical release is asserted.

WHAT WAS RESOLVED
The 2011 Census KS501EW qualifications, KS102EW age structure and QS102EW density bulk archives provide earlier baseline information. All counts and within-table denominators reconcile. Exact codes match 133 of the 135 candidate authorities. Northumberland and Gateshead use unmatched earlier codes and are excluded. Across the full 2016–2025 preparation, the restricted cohort covers 87.9–90.0% of collision counts. It does not meet the original 95% national headline gate. Known-mile coverage is not total England mileage coverage.

Official 2025 ONS district→county/unitary and district→police-force lookups establish whole-force membership. Two independently checked crosswalks, unique force per district, complete component-authority accounting, and common regional assignment avoid allocating mileage by population. Ten of39English forces fail full cohort requirements. The primary crime study also excludes Greater Manchester because its lagged crime contains a flagged recording-system period, leaving28forces. A prespecified29force sensitivity retains it. Census aggregation uses all-age population for age shares and density, residents16plus for qualifications, land area for density, and fixed2011resident weights for income/employment context. The latter are proxies, not official force deprivation averages.

CRIME DEFINITION
Use all explicit burglary subgroups and the archived offence-code allowlist, combining domestic/non-domestic and residential/non-residential classifications. Include historical codes with real counts even if the current reference calls them outcome-only. Calendar Q1 comes from fiscal Q4 of the preceding financial year; Q2–Q4 use fiscal Q1–Q3. Require all4quarters and all expected offence codes. Negative component revisions are retained; quarterly totals must be nonnegative. No missing observations are zero-filled. Annual totals2013–2024 reconcile for all39forces. The predictor is log(1 + burglary in year t-2 / fixed2011population *1000), not the contemporary annual crime rate. Reporting practice and classification change remain limitations. Burglary cannot establish a result for all crime.

MODEL AND CONTROLS
Fit negative-binomial NB2 counts with variance mu+alpha*mu^2 and log link. Offset log(target-year miles/100000), so exp(linear predictor) is rate per100000motor miles. Continuous terms are linear and training-standardised; no holdout feature selection, spline choice, calibration or tuning. Estimate dispersion in each training fit. Numerical ridge1e-6 penalises non-intercept coefficients; bounds on alpha1e-6 to10. Convergence and maximum-gradient checks must pass.

Baseline: log2011population density,2011shares under25 and65plus, two-year lagged car/taxi share of motor miles, log two-year lagged motor miles per road kilometre, linear year and regional indicators. This traffic intensity is an area proxy. Joint road class and urban/rural controls are absent and may explain apparent social effects. Do not interpret incremental coefficients as causal effects.

Deprivation uses only income/employment domain average scores from the panel's published2015/2019vintages, available before the model-year origin. No overallIMD, traffic-derived domain, composite subtraction or backdated2021education. Education uses the fixed2011no-qualifications share; Level4plus replaces it in a separate sensitivity. Census variables describe the2011baseline, not reconstructed later-year composition. A static baseline may become less representative over time.

History benchmark: log[(collisions t-2 + k*r)/(miles t-2/100000+k)], where r is the training aggregate rate and k is the median training lagged exposure in100000miles. Both are estimated only inside training. Pandemic history remains observed rather than imputed. Seen regions receive fitted effects; an unseen region receives the training-row-weighted average fitted regional effect.

TIMING AND VALIDATION
Model years2018–2025 allow two-year lag features from2016. Primary temporal holdouts2023,2024,2025 use expanding earlier training and exclude2020–2021. First training years2018,2019,2022 satisfy the three-non-pandemic-year requirement. 2025 is the final reserved temporal holdout. No model specification was changed after seeing results. Leave-one-region-out tests omit that region from all pre2025training and assess it in2025. Pandemic2020/2021stress fits use2018–2019only and are not primary validation.

Two-year event lags address publication delay but do not establish exact historical availability. Inputs are retrieved/revised2026series. Census tables were published before2016, but their currently retrieved bytes are not historical downloads. Therefore this is retrospective out-of-time validation, not a simulated live-vintage backtest. Target-year realised mileage is a conditional scoring exposure, not a forecast available at origin. Same-code geographic continuity is assumed; small boundary changes have not been independently quantified.

METRICS AND UNCERTAINTY
Compare nested models on identical rows. Gain=1-sum(Poisson deviance model)/sum(Poisson deviance comparator). Positive is better. Observed/expected=sum observed/sum predicted. Exposure-weighted absolute rate error=100000*sum(abs(observed-predicted))/sum miles. Do not treat percent deviance gain as percent fewer collisions or percent insurer claims savings.

95% intervals use2000paired resamples of English-region blocks over fixed held-out predictions, seed20261010. Keep every area's years together. There are only9independent region blocks and some force regions contain very few forces. Intervals are conditional on fitted models, exclude model-refitting and source measurement uncertainty, and are unadjusted for multiple comparisons. Dependence between nearby regions can make intervals optimistic. Within-one-region intervals are computationally degenerate and not interpreted; the website reports point estimates only. No confirmatory p-value/FDR pass is asserted.

An exploratory candidate requires combined temporal gain>=1%, lower95%bound>0, all3annualholdouts gain>=1%and observed/expected0.90–1.10, positive combined spatial gain and positive gain in at least5regions, and combined temporal calibration0.90–1.10. Otherwise: Not consistently supported. This label cannot promote original v1 hypotheses.

RESULTS
All294fits converged. No comparison passes every exploratory criterion.
In the133authority study, adding deprivation improves combined temporal deviance25.7%versus the reduced context baseline, but calibration and transfer fall short. Adding no-qualification share after deprivation improves temporal deviance17.4%, with uneven transfer. Against a history baseline, deprivation adds6.8%; adding qualifications after deprivation/history adds4.4%; the combined block improves11.0%but worsens combined unseen-region deviance4.3%.
In28primarycrimeforces, adding burglary after deprivation gives0.9%temporal gain with an interval crossingzero. With history included, burglary worsens temporal deviance5.3%. Including GreaterManchester yields0.7%worse and2.7%worse respectively. These are weak and unstable burglary results. Full tables, calibration, negative comparisons and regional results are retained.

REPRODUCE THE MODELS
Download reproduce-v2.zip and extract. The bundle has scripts/, db/ and public/ at its root, with the exact frozen inputs. From that root:
  python scripts/social-exploratory-model.py fit
Required: Python3,numpy,scipy. Original fitted versions are recorded in frozen-design.json. The fit command validates frozen hashes before using inputs. It reproduces numerical results, predictions, transforms and diagnostics; fittedAt and manifest timestamps change on re-execution. The prepare command refuses to overwrite the existing design. New sources/specifications require a new version; do not edit the published v2 inputs.

SOURCE EXTRACTION
Original source archives and detailed manifests are linked separately. Census extractor:
  python scripts/extract-social-census2011.py --panel db/research/social-factors-panel.json --output-dir /absolute/census-work
Place ks501ew.zip,ks102ew.zip,qs102ew.zip in that work directory to reproduce offline. The extractor checks pinned hashes; downloads only if an archive is absent.
Crime extractor:
  python scripts/prepare-social-force-crime.py --repo /absolute/repo --education /absolute/census-work/census2011-authority-features.json --out /absolute/crime-work
Copy the archived lad-pfa-2025.json,lad-county-2025.json,crime-geography.csv,offence-reference.ods and download-urls.json into crime-work. The archived HomeOffice workbook must occupy its source-register path under public/geo-evidence/ in the repo. The raw quarterly trace is supplied gzip-compressed. Source-input JSONs record geography memberships, exclusions, categories, assumptions, original hashes and official URLs. Model frozen-design.json independently freezes the final modelling inputs and folds.

NEXT EVIDENCE NEEDED
Historical joint road-class/urban/rural controls; stronger geographic transfer; annual population/vintage reconciliation; independently reviewed model specification. Preserve the original study and these unsuccessful comparisons. Any production pricing application needs separate insurer claims, exposure and governance validation.
