Test whether estimated off-street parking and garage use add predictive information after accounting for the type of area—and whether the pattern transfers across regions.
Phase 4 · rural–urban adjustment · spatial prediction checksDoes parking add information beyond the type of area?
Compare the same authorities after accounting for urbanisation, traffic, housing, car ownership and socioeconomic differences. The parking predictor remains an unvalidated estimate. These are retrospective area comparisons, not measured garage-use effects.
137 authorities685 authority-years · 2021–2025 · identical main-model cohort435,695 collisionsReported injury events on all public roads; damage-only crashes are absent9 regional holdoutsWhole regions and every year of their authorities held out together
0.92×95% authority-cluster interval: 0.40–2.10Fitted rate ratio per +10 percentage points of modelled parking, with full controls-31.3%Change in held-out deviance from adding parking Positive improves prediction; negative worsens it Region-block interval: -33.7–0.3%-98.2% to +49.3%Held-out gain across all 27 parking variants Predictive direction changes with assumptions.
The selected parking score does not improve pooled regional prediction. 2 of 9 held-out regions improve. A fitted coefficient and a predictive gain answer different questions. Neither establishes that putting vehicles into garages would reduce collisions.
The displayed effect is a local log-linear association scaled to a 10-point change, not a feasible intervention for every area. The full controls include the housing and car-ownership inputs from which the parking proxy was derived.
All injury collisions · same 137 authorities · reference housing mapping
Adjustment stage
Rate ratio per +10 points
95% authority-cluster interval
Held-out gain from adding parking
Parking alone
0.33×
0.30–0.37
Descriptive coefficient only
Rurality, density, road & traffic controls
0.73×
0.56–0.94
-71.5%
Full controls + parking
0.92×
0.40–2.10
-31.3%
Urban and full models also include year and region. The raw model contains parking alone. Prediction gains compare against the corresponding model without parking on exactly the same held-out observations.
Raw and adjusted decile patterns
Highest versus lowest parking decile: 0.13× raw, 0.96× after standardisation. A ratio of one means equal rates in the two groups.
Adjusted rates use observed ÷ expected collisions from the fitted full baseline without parking, multiplied by the relevant cohort’s pooled rate (within each rurality band for the grouped curves). This is descriptive standardisation, separate from the holdout test. It does not simulate moving an area to a different parking level.
RawAdjusted: observed / expected
All injury collisions · authority parking deciles · 2021–2025. Lowest parking on the left, highest on the right. Whiskers are conditional Poisson intervals; adjusted intervals treat the fitted expected counts as fixed and omit model and parking-measurement uncertainty.
Rates per 100,000 motor vehicle miles · deciles re-ranked on the complete-control cohort
Group
Parking share range
Authorities
Collisions
Million miles
Raw rate
Adjusted rate
Adjusted conditional 95%
D1
31.0–38.8%
14
52,797
26,187
0.2016
0.0370
0.0367–0.0373
D2
40.3–43.7%
14
42,242
49,204
0.0859
0.0352
0.0349–0.0356
D3
43.7–46.3%
14
37,274
82,465
0.0452
0.0361
0.0357–0.0365
D4
46.3–48.2%
13
56,495
126,636
0.0446
0.0405
0.0402–0.0409
D5
48.2–49.4%
14
53,959
164,502
0.0328
0.0388
0.0385–0.0391
D6
49.4–50.3%
14
47,956
178,944
0.0268
0.0345
0.0342–0.0348
D7
50.6–51.3%
13
46,876
196,565
0.0238
0.0365
0.0362–0.0369
D8
51.3–52.6%
14
24,967
79,730
0.0313
0.0358
0.0353–0.0362
D9
52.6–53.5%
14
32,331
135,821
0.0238
0.0378
0.0374–0.0382
D10
53.7–56.7%
13
40,798
156,037
0.0261
0.0356
0.0353–0.0360
Does the relationship differ by rurality?
Rurality is measured from Census populations in ONS-classified Output Areas, aggregated through the official geography lookup. It describes where residents live; it does not split road mileage into urban and rural travel.
40% urban
0.75×95% authority-cluster interval: 0.25–2.28Parking association per +10 points in the interaction model
70% urban
0.83×95% authority-cluster interval: 0.34–2.03Parking association per +10 points in the interaction model
95% urban
0.90×95% authority-cluster interval: 0.39–2.04Parking association per +10 points in the interaction model
Adding the interaction is a test of whether the parking association varies with urban population share. Sparse rural coverage limits how confidently we can compare the two settings.
Extra held-out gain from adding the interaction to the model already containing parking: -0.5%. Interaction-model held-out gain versus full controls without parking: -32.0%; region-block interval -34.4–1.6%. The 40% urban estimate is supported by relatively few rural authorities; interpret its interval with care.
Urban-dominated · 104 authorities · 0.0494 collisions per 100,000 miles
At least 80% of residents in urban Output Areas. These are analyst-defined bands.
RawAdjusted: observed / expected
Urban-dominated · parking quintiles within the group. Lowest parking on the left, highest on the right. Whiskers are conditional Poisson intervals; adjusted intervals treat the fitted expected counts as fixed and omit model and parking-measurement uncertainty.
Urban-dominated · rates per 100,000 motor vehicle miles
Group
Parking share range
Authorities
Collisions
Million miles
Raw rate
Adjusted rate
Adjusted conditional 95%
Q1
31.0–41.5%
21
73,435
48,381
0.1518
0.0485
0.0482–0.0489
Q2
41.6–46.3%
21
58,878
109,475
0.0538
0.0497
0.0493–0.0501
Q3
46.3–48.8%
21
71,566
165,127
0.0433
0.0546
0.0542–0.0550
Q4
49.1–51.7%
21
44,812
124,922
0.0359
0.0487
0.0483–0.0492
Q5
51.8–54.9%
20
30,268
116,955
0.0259
0.0483
0.0477–0.0488
Mixed · 29 authorities · 0.0249 collisions per 100,000 miles
50% to under 80% of residents in urban Output Areas. These are analyst-defined bands.
RawAdjusted: observed / expected
Mixed · parking quintiles within the group. Lowest parking on the left, highest on the right. Whiskers are conditional Poisson intervals; adjusted intervals treat the fitted expected counts as fixed and omit model and parking-measurement uncertainty.
Mixed · rates per 100,000 motor vehicle miles
Group
Parking share range
Authorities
Collisions
Million miles
Raw rate
Adjusted rate
Adjusted conditional 95%
Q1
48.2–50.0%
6
47,868
172,284
0.0278
0.0254
0.0252–0.0256
Q2
50.0–50.9%
6
32,358
143,211
0.0226
0.0249
0.0246–0.0252
Q3
50.9–52.4%
6
20,643
88,414
0.0233
0.0241
0.0238–0.0244
Q4
52.6–53.9%
6
20,553
102,641
0.0200
0.0260
0.0257–0.0264
Q5
54.1–56.7%
5
26,920
88,774
0.0303
0.0255
0.0252–0.0258
Rural-majority · 4 authorities · 0.0234 collisions per 100,000 miles
Under 50% of residents in urban Output Areas. These are analyst-defined bands.
Quintiles withheld: fewer than 15 authorities. The pooled rate is shown above; a rural quintile trend would be too thinly supported.
Which other effects add predictive information?
For each row, remove that block from the full baseline, then measure how much putting it back improves regional prediction. The remaining controls stay in place. Correlated predictors can substitute for one another, so this is conditional predictive value, not a causal ranking.
All injury collisions · baseline models exclude the parking score
Predictor block
Held-out gain
Region-block interval
Regions improving
Rurality & population density
+1.4%
-0.9–12.0%
6/9
Road exposure & traffic mix
-441.8%
-916.3–37.3%
5/9
Housing & car ownership
-110.0%
-134.4–16.5%
5/9
Income deprivation & education
-110.0%
-137.6–20.3%
6/9
Resident age structure
-12.0%
-13.1–3.6%
5/9
Junction density · 2026 sensitivity
+49.9%
-56.9–54.8%
5/9
Junction density is an addition to the full baseline, using April 2026 OS Open Roads. It is a retrospective sensitivity and cannot be treated as an input known before the 2021–2025 outcomes. Resident age and education are area context, not the characteristics of every road user.
Exact controls and source definitions
Urban population share; log population density and its square.
Trunk-road share of motor mileage; car/taxi, HGV and van mileage shares; log annual motor miles per road kilometre.
Income-deprivation average score and share of adults with no qualifications.
Resident shares under 25 and 65 or over.
Detached, terraced and flat household shares; households with no cars and with two or more cars.
Year and region effects. No authority fixed effect: the frozen parking predictor would be absorbed by it.
Network sensitivity: log(1 + junction and roundabout nodes per km²); ambiguous boundary nodes excluded.
Minor-road, speed-limit and urban-road-specific mileage have not been fabricated. Road context uses verified authority mileage and the official non-trunk split.
Can the pattern transfer to another region?
Each region is held out once, with all five years of its authorities. Feature scaling is fitted on training areas only. An unseen region gets the training-weighted regional effect. These are exploratory geographic checks using retrospectively available inputs; no future year has been held out.
Transfer is unstable. A model that fits these authorities can perform poorly in a different region. Large negative gains and observed / predicted ratios far from one are evidence of that failure, not results to discard. This model is not ready for operational risk prediction.
Full controls plus selected parking score versus full controls alone
Held-out region
Authorities
Deviance improvement
Observed / predicted collisions
East Midlands
8
-0.0%
1.06
East of England
11
+0.8%
0.98
London
33
-34.3%
0.25
North East
12
+1.8%
0.57
North West
22
-1.0%
0.78
South East
18
-0.1%
1.25
South West
9
-0.3%
0.88
West Midlands
12
-3.0%
0.91
Yorkshire and The Humber
12
-11.9%
1.09
Pooled observed / predicted: 0.56 with parking, 0.62 without. Exposure-weighted absolute rate error: 0.0346 with parking, 0.0288 without. One is the ideal observed / predicted ratio; lower error is better.
Annual scores from the same geographic holdouts
Geographic holdout predictions grouped by outcome year · not a time holdout
Year
Deviance improvement
Observed / predicted
2021
-32.7%
0.63
2022
-31.5%
0.59
2023
-31.3%
0.57
2024
-31.0%
0.52
2025
-30.8%
0.53
Does the parking assumption change the answer?
All injury collisions · full controls · reference housing mapping
Capacity and use
Allocation
Adjusted rate ratio
95% cluster interval
Held-out gain
Ample capacity
Independent housing and cars
1.19×
0.69–2.03
+21.3%
Ample capacity
More cars in lower-provision housing
1.08×
0.83–1.42
+10.9%
Ample capacity
More cars in higher-provision housing
1.06×
0.79–1.41
-9.1%
Constrained capacity
Independent housing and cars
0.29×
0.10–0.80
-2.2%
Constrained capacity
More cars in lower-provision housing
0.47×
0.25–0.90
+26.5%
Constrained capacity
More cars in higher-provision housing
0.60×
0.28–1.27
-20.4%
Reference assumptions · selected
Independent housing and cars
0.92×
0.40–2.10
-31.3%
Reference assumptions
More cars in lower-provision housing
1.03×
0.73–1.45
+6.7%
Reference assumptions
More cars in higher-provision housing
0.95×
0.65–1.39
-98.2%
All 27 variants, including alternative housing mappings
All model assumptions retained; no best-performing variant selected
Mapping
Capacity
Allocation
Adjusted ratio
Held-out gain
higher-provision
ample
independent
1.26×
+49.3%
higher-provision
ample
negative
0.97×
+5.5%
higher-provision
ample
positive
1.15×
+25.8%
higher-provision
constrained
independent
0.30×
-3.8%
higher-provision
constrained
negative
0.50×
+21.4%
higher-provision
constrained
positive
0.64×
-16.1%
higher-provision
reference
independent
0.90×
-45.8%
higher-provision
reference
negative
0.89×
-17.6%
higher-provision
reference
positive
1.02×
-3.5%
lower-provision
ample
independent
1.11×
+6.9%
lower-provision
ample
negative
1.02×
+4.5%
lower-provision
ample
positive
1.07×
+5.5%
lower-provision
constrained
independent
0.27×
-14.3%
lower-provision
constrained
negative
0.34×
-15.8%
lower-provision
constrained
positive
0.66×
-2.6%
lower-provision
reference
independent
0.76×
-77.8%
lower-provision
reference
negative
0.94×
-0.0%
lower-provision
reference
positive
0.97×
-48.6%
reference
ample
independent
1.19×
+21.3%
reference
ample
negative
1.08×
+10.9%
reference
ample
positive
1.06×
-9.1%
reference
constrained
independent
0.29×
-2.2%
reference
constrained
negative
0.47×
+26.5%
reference
constrained
positive
0.60×
-20.4%
reference
reference
independent
0.92×
-31.3%
reference
reference
negative
1.03×
+6.7%
reference
reference
positive
0.95×
-98.2%
Reference-only sensitivity checks
These checks always use reference capacity, reference housing mapping and independent allocation for the selected parking measure and outcome. They do not change with the capacity or allocation controls above.
All injury collisions · adjusted parking association per +10 percentage points
Check
Authorities
Rate ratio
95% cluster interval
Held-out gain from parking
Add junction density · 2026 snapshot
137
0.84×
0.38–1.87
-33.5%
Exclude London
104
0.70×
0.17–2.86
-3.2%
Non-trunk roads only
136
0.86×
0.37–2.00
-50.7%
Matched all-road comparator for the 136-authority non-trunk sample: rate ratio 0.91× (0.40–2.08); held-out gain -33.5%. This avoids attributing a sample change to road filtering.
Non-trunk mileage comes from DfT TRA8903. Collisions use the canonical non-trunk road flag. Any authority with an unknown trunk flag in any year is excluded from that entire sensitivity sample. Non-trunk roads include much more than residential streets.
Coverage, uncertainty and interpretation
Three of the Phase 3 authorities lack complete controls. Every main model uses the remaining 137 authorities and all five years. The parking shares, household inputs and rural classification remain fixed snapshots; no annual parking change is observed.
Adjustment does not validate the parking measure. The score is derived from housing and car ownership using national parking-provision assumptions. Added predictive value can reflect a useful transformation of those inputs. It is not independent evidence that actual garage use changes risk. All 27 variants remain visible.
Coefficient intervals allow repeated years within authorities. Prediction-gain intervals resample only nine regional loss blocks and indicate geographic instability. Neither includes parking-measurement error, uncertainty in DfT traffic estimates, unmeasured confounding or selective police reporting.
Frozen protocol and model specification
aim
Incremental spatial predictive information of an unvalidated parking proxy; not a causal garage-use effect.
design
Exploratory, frozen after Phase 3 descriptive results were seen. No confirmatory or future-year validation claim.
models
raw: Parking alone, no year/region controls; explanatory comparison
urban: Rurality, density and density squared, trunk mileage share, car/HGV/van mileage shares, log miles per road-km, year and region, plus parking
expanded: Urban model plus income deprivation, no qualifications, young/older resident shares, detached/terraced/flat shares and zero-/two-plus-car household shares
interaction: Expanded plus parking × (urban population share − 0.5)
network: Expanded plus log(1 + junctions/km²); April 2026 snapshot, retrospective sensitivity only
family
Negative binomial NB2, maximum likelihood; log(vehicle miles / 100,000) offset. Fixed tiny ridge 1e-6 on non-intercept coefficients for numerical stability; no hyperparameter tuning.
parking
Continuous proportion; association reported per +10 percentage points. Both off-street and inside-garage shares, all 27 Phase 2 variants. Housing/car inputs also enter the baseline; a derived parking score is not independently observed behaviour.
cohort
Same complete authorities in every stage and variant, fixed over 2021–2025. No imputation. Extra exclusions listed.
spatialValidation
Leave one of nine English regions out; all years for its authorities held together. Scaling learned in training only. Unseen-region effects use the training-authority-weighted mean. Every held-out observation gets one prediction per model. This is spatial transfer using retrospectively available inputs, not future prediction.
uncertainty
Full-fit coefficient intervals use an authority-cluster sandwich including the NB dispersion parameter; fixed-shape specification and measurement error not covered. CV gain intervals resample nine region loss blocks 2,000 times: descriptive instability intervals, not independent confirmatory inference.
metrics
Percentage reduction in held-out Poisson deviance versus the same-sample baseline, plus observed/expected and exposure-weighted absolute rate error. Positive gain improves prediction; negative gain worsens it. No scenario selected as best.
adjustedCurve
Observed / expected (expanded baseline WITHOUT parking, full-sample fitted) × the cohort pooled rate. This indirect standardisation is descriptive and in-sample. Conditional Poisson intervals ignore uncertainty in expected counts; they are not causal effect intervals.
ruralGroups
Analyst-defined population bands: urban >=80% urban residents, mixed 50–<80%, rural <50%. Quintiles within groups of at least 15 authorities; smaller groups show pooled rates only. Ties kept together. Resident rurality is not road-mileage rurality.
nonTrunk
Separate reference-model sensitivity with TRA8903 mileage × 1,000,000 and canonical STATS19 trunk flag 2. Require zero unknown trunk flags across all five years per authority; compare to all-road fits on this identical subcohort. Non-trunk is not synonymous with residential.
unknown
Parked and other endpoints are recorded lower counts. Unknown involvement remains separately tabulated and is never reclassified as other. Additional reference sensitivity assigns all unresolved cases to each endpoint separately.
limits
No new LSOA mileage. Injury collisions only. Parking use unvalidated; 2021 households and 2024 parking provision are retrospectively applied. Network snapshot is 2026. No claim of year-ahead validity, causation, or driver-level demographic effects.
Download the analysis and reproduce it
Source bytes, geography joins, frozen folds, every scenario effect, fitted coefficients and held-out predictions for the nine reference-housing variants are available. The model runs offline using NumPy 2.3.5 and SciPy 1.17.0. The preparation guide records the separate geospatial dependencies.