Johan Strydom · 10 October 2026 · London-first regional modelling · Exploratory research
Prioritise the regional baseline; keep social effects under review
Training-only selection chose the complete London baseline in all three assessment windows and all 33 borough holdouts. It improves pooled London deviance by +53.46% versus the national baseline. Continuous social features together add +14.23%, but every social-feature uncertainty range includes zero.
The experiment is implemented and reproducible. It compares national, coefficient-shrinkage and complete London baselines before adding qualifications, income and employment. These are road-location collision rates per motor-mile; they are not individual driving-risk estimates. Crime was not available in the matched borough panel and was not substituted with a proxy.
1. What was fitted and how selection was protected
The frozen panel has 133 English authorities and eight years, including 33 London authorities. The outer assessment years are 2023, 2024 and 2025; fitting uses earlier years from 2018, excluding 2020 and 2021. Each comparison uses identical assessment rows and realised motor-mile offsets. Inner and Outer London follow the London Plan 2021 Annex 2: 14 and 19 authorities respectively.
For each outer window, five fixed borough groups are held out across every training year. Candidate models predict each held-out group's latest training year. The selector uses summed Poisson deviance and chooses the strongest pooling within 1% of the best inner score. National anchors, history priors, scaling and cuts are relearned after each exclusion. Duplicate bootstrap copies of the same original borough stay in one group. The target-year outcome never enters selection.
Coefficient shrinkage uses a two-stage empirical penalty: lambda/2 times the squared distance between London's standardised coefficients and the refitted national London predictor. Lambdas are 0, 1, 10, 100 and 1000, with infinity returning exact national predictions. The penalty includes the intercept and Inner/Outer term; the latter has a zero national anchor. Local NB2 dispersion is estimated for finite candidates. This is not a fully Bayesian hierarchical model. A separate complete London candidate also learns the collision-history prior from London and includes Inner/Outer.
Recorded amendment: V1 initially held the national history-feature construction fixed when comparing London coefficients. After its three point assessments were inspected, V2 added complete London feature construction to the candidate set. V1 results and both frozen protocols remain in the package. Nested selection prevents direct assessment-year tuning inside each fit, but cannot turn this repeatedly inspected dataset into fresh confirmation.
2. Regional baseline results
All baseline gains above are measured against the same national model on London assessment rows. Partial pooling is selected only among positive finite penalties: 1000, 1000 and 100. The expanded selector chooses complete London construction for all three years. “Previous local” exactly reproduces the earlier benchmark without Inner/Outer; it is not an extra candidate in the expanded selector.
The selected model's pooled O/E is 1.006, compared with 0.920 nationally. Its mileage-weighted absolute error falls from 0.01586 to 0.01050 collisions per 100,000 miles. The pooled refit range is +3.16% to +73.09%; annual ranges are -63.48% to +66.60% in 2023, +0.00% to +80.93% in 2024, and +8.83% to +78.86% in 2025.
3. The collision-history prior is part of the baseline
The inherited history predictor is log((lagged collisions + prior exposure × prior rate)/(lagged exposure + prior exposure)). The prior rate is training collisions divided by training motor-miles; prior exposure is median training lagged mileage. National and London training populations give materially different priors:
Keeping national history construction while freeing London coefficients yields a +29.73% pooled gain; complete London construction with Inner/Outer yields +53.46%. Because numerical standardisation of unpenalised slopes preserves the fitted function apart from the tiny ridge, the substantive history prior is an important contributor. This comparison does not identify a causal transport mechanism or prove which omitted road-exposure control is responsible. Simply adding a London intercept would not reproduce the result: the original national model already has regional intercepts.
4. Social features retested after selecting the baseline
The chosen baseline and its penalty are fixed before testing social blocks. Each social model then refits the baseline coefficients and its added terms on London training rows. Qualifications means the Census 2011 share of residents aged 16+ with no qualifications. Deprivation jointly includes income and employment, using only the historical editions available before the outcome year. Continuous features are centred/scaled from training rows. Bands retain national D1–8, D9 and D10 with training-only cuts; D10 is the lowest deprivation or no-qualifications share.
The leading follow-up is the combined continuous block. It improves all three years and both Inner/Outer point comparisons. Its pooled gain is +14.23%; the independently excluded-borough check gains +17.94%. Its refit range, -8.67% to +26.14%, still includes deterioration. Qualifications alone as a linear term worsens each year and the borough check. Qualification bands improve each temporal year, but their borough gain is only +0.88%.
Income and employment are highly correlated within London (0.973 for the 2015-vintage scores and 0.964 for the 2019-vintage scores). Their continuous joint-model coefficients have opposite signs. Treat them as a predictive block, not separate causal deprivation effects. The continuous qualification coefficient is also conditional on the full baseline and correlated social controls.
Qualifications added after continuous deprivation yield +7.34% pooled and +6.13% in borough holdout, but the interval still crosses zero. Combined bands worsen the borough test by 16.7%. These results do not support another outcome-driven merging of bands at this stage.
5. Within London and central-borough sensitivity
Removing City of London and Westminster triggers a full reselection: lambda 100 for 2023, the national model for 2024, and complete London for 2025. The selected baseline's pooled gain drops from +53.46% to +11.38%, with a negative 2023 result. The combined continuous increment drops to +5.23% and is negative in 2024. This is a material limitation on stability. It does not justify excluding those boroughs from the main population. Holding the complete local candidate fixed instead of reselecting gives a +26.98% baseline gain for the same reduced population.
6. Uncertainty, support and numerical checks
399 authority-history resamples were attempted with national-region strata and separate Inner/Outer London strata. Each draw refits the national anchor, all nested choices, transformations and social terms. 395 complete paired draws enter the marginal percentile ranges. Four draws have optimizer failures in five folds and were not replaced or silently accepted:
The unsuccessful fits returned abnormal optimiser termination despite small reported projected gradients; the prespecified requirement for optimizer success was retained. 58,366 successful fits were recorded in completed bootstrap folds, including 1,204 rank-deficient designs retained under the fixed numerical ridge. Partial work inside unsuccessful folds is not included in this recorded-fit count. 4,110 bootstrap social fits fail a support or full-rank check.
To assess the four missing draws, a post-processing bound places them all in the worst or best tail without fabricating fitted values. The selected-baseline pooled percentile endpoints could then extend to +0.63% and +73.88%. All social ranges continue to cross zero. This bounds the missing-draw effect; it does not repair unsuccessful estimation or account for bootstrap Monte Carlo error.
All temporal point designs have full rank. The deprivation-band and combined-band models lose rank in the Kingston upon Thames borough holdout. Every band model fails the inherited minimum-ten-authority support rule somewhere: qualification D9 contains seven London authorities; current income D9/D10 contain three/two, and employment D9/D10 seven/three. Repeated years do not increase the number of independent authorities. All three continuous specifications meet the point support and rank checks.
The bootstrap treats authority histories as independent within the stated strata; it does not model residual dependence between neighbouring boroughs. The three annual windows overlap, and there is no multiplicity correction. The new bootstrap seed and nested selection differ from the previous report; a changed lower endpoint is not new independent evidence. No reserved future outcomes were accessed.
7. Decision and implementation sequence
Carry the selected regional baseline forward as the exploratory reference. The baseline passes the prespecified pooled candidate gate, with central-borough and early-year sensitivity prominently retained. No social block passes all checks. Keep the combined continuous block as the leading research comparison and qualification bands as a secondary explanatory view; do not apply either as an established risk multiplier.
- Data lab: consume the included
data-lab-results.json and prediction/metric exports. Present National / Selected regional / Regional + social comparisons; show annual and borough validation separately, retain Inner/Outer filtering, and expose the frozen protocol, amendment, support and failed-fit counts. Use “exploratory candidate” as the baseline status and “not consistently supported” for the social additions.
- Wider website: publish a methodology/evidence summary when integrating the research release. Explain that context and collision history explain much of the observed area contrast. Keep illustrative deciles separate from validated predictive features. Do not convert area associations into driver scores, underwriting decisions or proven causal statements.
- Next regional experiment: apply a frozen version of this framework to the South East, which has 18 authorities in the cohort, then the other regions. Relearn region-appropriate history priors and use stronger pooling or fewer regional deviations where support is smaller. Select complexity inside region-aware training folds and assess each region before producing a combined national conclusion. Treat this as a new experiment, not permission to reuse London's fitted coefficients elsewhere.
- Evidence improvement: obtain historical road-class × urban/rural exposure and test whether it reduces apparent social effects. Crime needs a historical borough-aligned panel with recording-break checks; the earlier force-level crime extension cannot be silently assigned to boroughs. LSOA modelling still requires credible all-road mileage. Register truly uninspected future validation before any production promotion.
This delivery contains analytical implementation and a publication-neutral integration payload. It does not change or deploy the existing website.
8. Reproducibility and provenance
Inputs are copied from the preceding within-region analysis, preserving its frozen 133-authority design, London classification and original prediction archive. The original numerical NB2 and decile modules are unchanged. National B predictions and the prior local benchmark were reproduced; the analytic penalised gradient was checked numerically on synthetic data. Both protocols, code/input hashes, per-fold selection scores, fitted coefficients, bootstrap histories and failures are archived. The ZIP includes the source lineage already embedded in the original frozen design.
Run the archived README commands in an extracted copy. Bootstrap checkpoint directories are omitted from the ZIP to avoid duplicating the complete compressed refit archive. Re-running the bootstrap reconstructs all 399 draws. Reports and charts are derived from saved results; all comparison denominators are explicit.