Map

Interactive map

Explore province-level OOF R², A/B/C performance classes, and feature-importance layers in a single map.

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Model performance

Province OOF R² (Grouped CV)

Province-level Out-of-Fold R² values. Selected model: Random Forest.

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Province OOF R² report
Classification

Province performance classes (A/B/C)

A: Use as is. B: Moderate regularization (λ=0.2, γ=0.2). C: Strong regularization (λ=0.5, γ=0.4).

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Province A/B/C classes
Feature importance

Feature-importance composition (province level)

Shares of NDVI, NTL, SENT1, SENT5, Population, and Surface. Use the embedded interactive chart and maps below to inspect values.

Interactive stacked bar chart

Six feature shares per province (stacked). Hover to see province name and percentages.

Feature-importance composition (stacked, normalized)
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Interactive map — pie chart

Feature shares shown as a pie chart for each province. Click a province for details.

Türkiye — Province-level feature-importance shares (pie)
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Static figures

Static versions of the same results.

Feature importance — pie map
Feature importance — single map (pie)
Six-panel maps
Province-level importance shares (0–1) — six maps
District GDP

District GDP map (2023)

RF-based district-level GDP allocation. Use the province filter to focus on a single province or the full map; the color scale updates accordingly.

Open the map Static figure
District GDP map
Tables

Tables

Numerical results for model comparison and robustness variants. Metric definitions and table intent are summarized below.

Table 1. Grouped cross-validation performance by model type

Model Type N (provinces) N (districts) Features CV R² CV MSE CV MAE Selected
ElasticNetLinear8197360.4580.3310.303—
SVRKernel8197360.4480.3370.285—
CatBoostBoosting8197360.5570.2700.240—
RFBagging8197360.5620.2670.244Yes
XGBoostBoosting8197360.5160.2950.259—
LightGBMBoosting8197360.5370.2830.253—
Metrics: CV R² = R² computed via grouped cross-validation (grouped by province); CV MSE = mean squared error; CV MAE = mean absolute error. Higher R² and lower MSE/MAE are preferred.
Purpose: Six model families are compared on the same dataset and feature set. Random Forest (RF) is selected with the highest CV R² (0.562) and the lowest CV MSE/MAE; subsequent district-level GDP allocation is reported using RF.
Brief takeaway:
  • RF slightly outperforms CatBoost and LightGBM in CV R², while linear models (ElasticNet, SVR) perform substantially worse.
  • RF also achieves the best MSE and MAE, indicating lower prediction error.
  • Grouped CV reduces leakage risk by keeping provinces separated across folds.

Table 2. Selected model summary (RF)

N (provinces) N (districts) N (features) CV R² CV MSE CV MAE
8197360.5620.2670.244
Metrics: Sample sizes (81 provinces, 973 districts) and feature count (6) are fixed; values summarize the RF results under grouped CV.
Purpose: A one-row overview of the final setup used in the paper.
Brief takeaway:
  • R² ≈ 0.56 indicates moderate explanatory power at province-level grouped CV; remaining variance may reflect within-province structure and measurement uncertainty.
  • MSE (0.267) and MAE (0.244) indicate acceptable error magnitudes given the target scale.

Table 3. Robustness variants — JS and L1 distance

variant JS_mean JS_median JS_max L1_mean n_province
GAM_minus2.61E-068.10E-073.99E-050.002781
GAM_plus2.57E-068.72E-073.97E-050.002781
LAM_minus2.02E-067.67E-072.10E-050.002581
LAM_plus1.96E-068.40E-072.22E-050.002581
THR_Aminus9.37E-0603.32E-040.001581
THR_Aplus1.62E-0501.15E-030.001681
THR_Bminus3.54E-0802.87E-060.000081
THR_Bplus2.04E-0601.45E-040.000581
Metrics: JS = Jensen–Shannon divergence (difference from reference feature-importance distribution); L1_mean = mean L1 distance; lower values indicate closer agreement with the reference distribution.
Purpose: Quantify how feature-importance shares change under gamma/lambda (GAM/LAM) and threshold (THR) perturbations. THR_Bminus is the most stable variant with minimal JS and L1.
Brief takeaway:
  • THR_Bminus is closest to the reference (JS_mean ≈ 3.5e-08; L1_mean = 0).
  • THR_Aplus yields the largest deviation (JS_max 1.15e-03), indicating A-class threshold changes shift feature importance more.
  • GAM/LAM variants remain close to each other, suggesting stability within a reasonable parameter range.
Correlations

GDP vs. SES and RWI (2023)

Relationship between district GDP and socioeconomic score (SES) / relative wealth index (RWI).

GDP vs SES
GDP vs RWI

Empirical validation of SEDI’s core assumption (NUTS-3)

Purpose: test whether the SEDI distribution mirrors macroeconomic reality using official GDP per capita (development density), rather than total GDP (population-confounded).

SEDI vs GDP per capita: 2011, 2017, and 2024/25 validation
Province-level SEDI–GDP per capita correlation: 2011 r=0.887 (R²=0.787), 2017 r=0.882 (R²=0.779), 2024/25 r=0.886 (R²=0.785).