How Local Relationships Themselves Shift as a City Changes
Same Grid, a Different Question From MGWR
The MGWR & Spatial Durbin case study asked whether relationships are stationary across space. This one holds the spatial question fixed — single adaptive bandwidth, bisquare kernel, chosen fresh each year — and asks a temporal question instead: for the exact same covariate, in the exact same grid cell, does its local coefficient drift as 2015 becomes 2025 becomes 2035?
All 1,493 cells, live — pick a metric, a layer (local R² or a per-cell coefficient), and a year, then click between 2015 / 2025 / 2035 to compare the same cross-section over time. Hover any cell for its exact value. All nine models (3 metrics × 3 years) are refit directly from the source shapefiles at each year's known optimal bandwidth — not a static export.
A Tightly Local Relationship (145–205 Neighbours)
Built-up PD's optimal adaptive bandwidth stays small across all three years — between 145 and 205 nearest neighbours out of 1,493 cells — meaning the covariates that predict built-up fragmentation act on a genuinely local scale, consistent with the low global R² (0.55–0.59) and large MGWR improvement (+0.22 to +0.34) found in the companion regime study.
Differencing the coefficient surfaces between years isolates where a predictor's local effect — not just the underlying metric — is shifting. The Built_AI coefficient swings from a strong negative pocket in the west (2025→2015) to a strong positive pocket near the same area (2035→2025): the relationship between built-up aggregation and patch density didn't just move in strength, it flipped direction in the same location a decade later.
A Nearly Global Relationship (608–860 Neighbours)
Vegetation Cohesion's adaptive bandwidth is 3–5× larger than Built-up PD's — 608 to 860 neighbours — meaning its predictors act far more uniformly across the city. This tracks exactly with the companion MGWR study: Veg. Cohesion is already well explained by a single global relationship (R² 0.88–0.92), so there's simply less local structure left for a spatially-varying model to find.
Local Again, and Distinct From Its Cohesion Counterpart
Vegetation PD's bandwidth (194–253 neighbours) sits close to Built-up PD's, not Vegetation Cohesion's — despite both being vegetation metrics. Patch density and cohesion measure different things (fragmentation count vs. connectivity), and they respond to the same covariates at genuinely different spatial scales.
Note: the source notebooks' year-over-year change grids for Veg. Cohesion and Veg. PD were found to be stale duplicates of one another on inspection (a re-run/caching artefact, not a modeling result) and are excluded here pending a re-run — only the independently-verified per-year snapshot coefficients above are shown for these two metrics.