SPATIAL ROBUSTNESS ANALYSIS PROTOCOL

1. Regional robustness
- MAIN210 is dominated by Lijin (n=121) and Kenli subregional source lane (n=80).
- For each dominant region, report raw Spearman rho between SRSI2000 and Y3.
- Coordinate-adjusted descriptive association: within region, fit separate quadratic UTM-coordinate surfaces to Y3 and SRSI2000; correlate the two residual vectors with Spearman rho.
- This is an association diagnostic, not a causal adjustment.

2. Matched 15-km nested incremental prediction
Frozen spatial structure:
- Outer folds: headline15km_fold = 1..5.
- Inner folds: inner4_when_outer{outer} = 1..4 inside each outer training set.

Tree models:
- Algorithms: XGBoost and Random Forest.
- Hyperparameter candidates: the same three candidates preserved in A2.66_XGB_RF_INNER_TUNING_LOG_v1.csv for Y3 / Path A.
- Each feature set is tuned independently within the four inner folds of each outer training fold.
- Feature sets include coordinates only; coordinates + five non-SRSI Path A covariates; coordinates + all six Path A covariates.
- Report pooled OOF RMSE, MAE, R2, Spearman, fold metrics, and residual Moran I.

Linear nested comparison:
- Within each outer training fold, standardize UTM x/y, generate second-order polynomial coordinate terms, and fit linear regression.
- Add five non-SRSI Path A predictors after training-fold standardization.
- Then add SRSI2000 after training-fold standardization.
- Report pooled OOF metrics. The SRSI-specific increment is R2(full) - R2(coordinates + other Path A).

3. SRSI spatial structure
- Report Spearman correlations of SRSI2000 with UTM easting, UTM northing, and distance to the 2000 coastline.
- Predict SRSI2000 using only quadratic UTM coordinates under the frozen 15-km outer folds.

4. Predictor-only spatial-similarity diagnostic
This diagnostic uses no outcomes and is descriptive only.
- K = 6 Path A baseline predictors.
- Standardize each predictor across MAIN210: z_ik = (x_ik - mean_k) / sd_k.
- For a settlement pair i,j define:
  S_ij = (1/K) * sum_k(z_ik * z_jk).
- Summarize mean and median S_ij by center-distance bands.
- This outcome-free diagnostic is descriptive only and is not used to claim that 15 km is an empirically optimal decorrelation distance.

5. 4-km greedy thinning-order robustness
For each outcome-independent ordering:
- rc_id ascending
- easting ascending
- easting descending
- northing ascending
- northing descending
- pseudorandom order with fixed seed 20260822
Algorithm:
1. Start with an empty retained set.
2. Visit candidate settlements in the chosen ordering.
3. Retain candidate if its center is at least 4.0 km from every already retained center; otherwise skip it.
4. Continue until all candidates have been visited.
- Theoretical overlap of two equal 3-km circles at 4-km center separation is <=21.91%.
- Evaluate Path A using the frozen fixed-candidate sensitivity parameters and the original 15-km fold labels.
- Also calculate a quadratic coordinate baseline and 8-nearest-neighbor residual Moran I with 199 permutations.

6. 10/15/20-km block-geometry sensitivity
- This remains DESCRIPTIVE.
- For each Path A/B and algorithm, choose the candidate with the lowest mean archived inner-CV RMSE across the five original 15-km outer-fold tuning records.
- Hold that candidate fixed and change only the frozen block geometry (10, 15, 20 km).
- These values are not presented as new unbiased nested-generalization estimates.
