Two case studies in applied spatial statistics: a Moran's I / LISA diagnostic pipeline built for the Ruhr region (Germany), and a four-dataset methods showcase covering choropleth classification, autocorrelation, point-pattern density, and spatial inequality.
A Moran's I / Local Indicators of Spatial Association (LISA) pipeline built as a methodology precursor to a Dortmund LULC / spatial-econometrics thesis — run here on a synthetic 810-cell grid over the real Regionalverband Ruhr (RVR) boundary to validate the workflow before applying it to real thesis variables.
KNN weights → Global Moran's I → Local Moran's I (LISA)
Global spatial autocorrelation: I = 0.559 (p = 0.001)
A K-nearest-neighbours spatial weights matrix was built over the grid, a spatial lag computed, and Global Moran's I tested against a permutation-based reference distribution — a strongly significant positive value, indicating the surface is far from spatially random.
Grid cells810Global Moran's I0.559p-value0.001
Synthetic surface (LST/NDVI-style values) over the RVR boundaryPermutation reference distribution & Moran scatterplot
Local Moran's I decomposes the global signal into per-cell cluster types (High-High / Low-Low / High-Low / Low-High) and flags which clusters are statistically significant — the basis for targeted, rather than region-wide, follow-up analysis.
Note: run on a synthetic grid as a workflow validation step — real Kreise-level thesis variables (LULC change, built-up density) are the next input, per the project README.
02 — Spatial_Methods_Portfolio
Spatial Methods Portfolio
Four independent case studies, each pairing a core spatial-statistics method with a real dataset: choropleth classification (Sri Lanka), spatial autocorrelation (UK), point-pattern density (Japan), and spatial inequality decomposition (US).
UK · Brexit referendum, 2016
Spatial Autocorrelation of the Leave Vote
Local-authority-level "% Leave" share, classified by quantiles, then tested for spatial clustering via KNN weights and Global/Local Moran's I — the canonical Moran's I / LISA workflow applied to a real, high-salience dataset.
Leave vote share by local authority (quantile classification)LISA diagnostic — Scotland reads as a strong Low-Low (Remain) cluster, the English Midlands/East as High-High (Leave)Open interactive Brexit map
Sri Lanka · GND-level population, 2001 vs 2011
Choropleth Classification Method Comparison
Nine classification schemes (Equal Interval, Quantiles, Std. Mean, Maximum Breaks, Box-Plot, Head/Tail Breaks, Jenks-Caspall, Fisher-Jenks, Max-P) were fit to the same right-skewed population distribution and compared via the Absolute Deviation around Class Medians (ADCM) fit statistic — the distribution shape below is exactly why classifier choice matters.
Hexbin density, KDE surfaces, and centrography (mean/median center, standard deviational ellipse) applied to photo-point data, plus formal tests for complete spatial randomness (Ripley's G, quadrat chi-square) — moving beyond visual density to statistically confirm the clustering is non-random.
Points10,000Peak density zoneMinato/Shinjuku
Hexbin density — photo activity concentrated around central TokyoCentrography — mean/median center and standard deviational ellipseOpen interactive density map
US Counties · per-capita income, 1969–2017
Spatial Inequality Decomposition
Gini index, Lorenz curves, and Theil decomposition (between vs. within Census region) applied to a county-level per-capita income panel spanning nearly 50 years, alongside Queen-contiguity Global Moran's I computed for every year in the series.
Moran's I, 19690.65Moran's I, 20170.42TrendConverging
Per-capita income by county (quintile classification)Global Moran's I by year — spatial clustering of income has weakened steadily since 1969
The decline in Moran's I over five decades suggests county-level income patterns have become less spatially clustered over time — but the Theil decomposition shows the "within-region" component of inequality has been rising since 2010, even as the "between-region" gap continues to shrink.
03 — MGWR_SDM_Regime_Analysis
MGWR & Spatial Durbin Regime Analysis
Does one model fit the whole city? Multiscale GWR and a five-city-sector Spatial Durbin Model applied to the same 1,493-cell Dortmund landscape-metrics grid (Built-up Patch Density, Vegetation Cohesion, Vegetation Patch Density × 2015/2025/2035) — testing whether landscape-metric drivers are spatially stationary or structurally different by sector.
MGWR: local vs. global relationships
MGWR closes up to 60% of the unexplained variance a citywide model leaves behind
Built-up and Vegetation Patch Density are barely explained by a single global relationship (R² ≈ 0.52–0.59) — letting each covariate's coefficient vary spatially via its own optimal bandwidth lifts fit to R² 0.81–0.89. Vegetation Cohesion, already well explained globally (R² 0.88–0.92), gains comparatively little from local variation.
The same variable can push a metric up in one sector and down in another
Grouping Dortmund's 12 Stadtbezirke into five sectors (Core/North/East/South/West City) and fitting a separate Spatial Durbin Model per sector, a Chow test confirms the sectors are structurally different (p < 0.001 for all nine metric/year combinations) — not just noisier versions of one citywide model. A landscape-shape-index change that suppresses built-up density directly can spill over to increase it in neighbouring cells, and the size — sometimes the sign — of that effect flips between sectors.
A companion question to the MGWR/SDM study above: rather than asking whether relationships vary across space, this fits single-scale adaptive GWR independently for 2015/2025/2035 and differences the results — do local coefficients themselves drift as the city develops?
Adaptive bandwidth by metric
Built-up and Vegetation PD are local (145–253 neighbours); Vegetation Cohesion is nearly global (608–860)
The bandwidth GWR selects for each metric is itself a diagnostic: Vegetation Cohesion needs 3–5× more neighbours to fit well, meaning its relationships are far smoother across space — consistent with its high global R² in the MGWR study. Differencing Built-up PD's coefficients year over year shows a covariate's local effect not just weakening or strengthening, but flipping sign in the same location a decade later.
Regime Landscape Metrics — 35 Years of Fragmentation
Raw FRAGSTATS fragmentation metrics (not a modelled outcome) computed directly from land-use rasters, 2000–2035, by city-sector regime — rising steadily through 2020, then predicted to reverse. A formal structural-plausibility check flags which of the model's own forecast transitions fall outside each regime's historical envelope.
Structural plausibility check
Edge Density is flagged as implausible in all 5 regimes for 2025→2030
Comparing each regime/metric's predicted 5-year rate of change against its own historical mean ± SD annual rate surfaces exactly which forecast transitions to trust — Cohesion and Largest Patch Index are never flagged; Edge Density is flagged everywhere in the 2025→2030 transition.
The same fragmentation metrics as above, at native 1,493-cell resolution instead of 5-regime averages — so within-district variation a regime mean hides (South City's Patch Density ranges from 3.96 to over 2,000 across its own cells, versus one regime number of 17.49) is directly inspectable.
Grid vs. regime resolution
Every cell, individually, 2000–2035
Quantile-classed choropleth robust to boundary-sliver outliers, with an info panel showing all 5 grid-native metrics (SHDI, Built-up PD, Built-up AI, Vegetation Cohesion, Edge Density) for any hovered cell at the selected year.
