From local to global explainability: linking regression contributions with spatially adjusted SHAP

When artificial intelligence models are asked to explain themselves in the spatial sciences, the results have often been less than transparent. A new study published in the journal Machine Learning with Applications introduces a method called Spatially Adjusted SHAP, or SA-SHAP, that promises to bridge a long-standing divide between classical geographically aware statistics and modern machine learning interpretation. The research, authored by Mohammad H. Vahidnia, demonstrates that carefully adjusted explanations from a black-box model can closely reproduce the spatially varying contributions produced by one of geography’s most trusted statistical tools.

At the heart of the problem lies a fundamental tension in geospatial modeling. Relationships between environmental or socioeconomic predictors and the outcomes they influence frequently shift from one location to another, a phenomenon known as spatial heterogeneity. For decades, researchers have handled this with Geographically Weighted Regression and its multiscale extension, MGWR, which estimate a separate regression coefficient at every location, allowing the effect of a variable such as rainfall or population density to grow stronger in one region and weaker in another. These local coefficients are transparent and easy to map, but the underlying models are linear, computationally constrained, and sometimes less accurate than modern alternatives.

Machine learning models, particularly gradient-boosted tree ensembles like XGBoost, routinely outperform such linear frameworks on predictive tasks. Yet their internal complexity makes them opaque. To open the black box, researchers have turned to explainable artificial intelligence, and especially to the SHapley Additive exPlanations framework. SHAP, which descends from the Shapley value concept in cooperative game theory, assigns each feature an additive contribution to a prediction by averaging its marginal effect across all possible subsets of features. The approach is theoretically grounded and works both for individual predictions and for aggregate feature importance, but it was never designed with geography in mind.

The complication arises when spatial coordinates are fed directly into machine learning models as predictors. Doing so allows the model to capture spatial context, and studies in landslide susceptibility, earthquake probability, land surface temperature, urban fire risk, and ride-hailing demand have all combined XGBoost with SHAP to reveal how drivers of a process vary across a map. However, a growing body of critique warns that raw longitude and latitude often act as positional surrogates rather than genuine causal factors, and global SHAP outputs become harder to interpret once geographic components and their interactions with non-spatial features are decomposed across many encoded spatial variables.

Vahidnia’s contribution is a methodological reallocation rather than a new game-theoretic formulation. In the SA-SHAP approach, the raw SHAP value of a non-spatial predictor is combined with its SHAP interaction values with the spatial features, so that the influence a predictor exerts jointly with location is credited back to the predictor itself. Formally, the adjusted contribution equals the feature’s primary SHAP value plus the sum of its interactions with every spatial component in the model. The result is a feature-level spatial explanation, analogous to the local contribution computed in MGWR, where a coefficient at a location is multiplied by the predictor’s value there. The author emphasizes that this reallocation is an interpretability device, not a causal decomposition, since SHAP interaction values reflect both the fitted model and the joint distribution of the predictors.

To test whether these adjusted explanations genuinely correspond to the contributions from classical local regression, the study relied on carefully controlled simulation. Two synthetic datasets were generated on a regular two-dimensional grid of thirty by thirty cells, one with four predictors and one with seven. The true coefficients were designed as distinct mathematical surfaces, including linear trends, quadratic paraboloids, sinusoidal oscillations, sharp sigmoidal transitions, and localized Gaussian bumps, ensuring that each variable behaved according to a different form of spatial heterogeneity. Because the ground truth was known, the agreement between methods could be measured against reality rather than against another estimate. A second, more demanding experiment also injected mild nonlinear terms, a quadratic effect, a sine transformation, and a pairwise interaction, to probe robustness beyond MGWR’s linear assumptions.

The machine-learning side of the comparison used XGBoost trained with four different ways of representing space: raw coordinates, Moran’s Eigenvector Maps derived from a spatial weights matrix, radial basis function kernels centered across the study area, and Space2vec, a Fourier-style embedding that maps coordinates into sine and cosine features at multiple frequencies. MGWR was fitted in parallel using adaptive bisquare kernels and backfitting optimization, with bandwidth selection minimizing the corrected Akaike Information Criterion. The resulting bandwidths, ranging from roughly 100 to nearly 500 cells, confirmed that each predictor operated at a distinct spatial scale, and MGWR achieved coefficients of determination around 0.94 and 0.91 for the two simulations.

The results were strikingly consistent. At the local level, cell-by-cell scatterplots comparing MGWR contributions with SA-SHAP contributions yielded coefficients of determination mostly above 0.9 in the four-variable case, with values ranging from 0.835 to 0.976 across encodings, and similarly high values between 0.845 and 0.962 for the seven-variable problem. At the global level, the beeswarm plots of feature importance, a visualization familiar to any SHAP user, produced exactly identical importance rankings under both MGWR and SA-SHAP and under all four spatial encodings. In the four-variable experiment, the ordering x2, x1, x4, x3 held everywhere, with mean contributions and percentage shares nearly matching between the statistical and machine-learning paradigms. In the seven-variable case, the ranking x4, x2, x6, x1, x7, x3, x5 was likewise invariant.

Encoding choice itself proved largely irrelevant to the conclusions. Pairwise Spearman rank correlations computed across the full SA-SHAP contribution matrices from the four encoding strategies all exceeded 0.95 in both experiments, indicating that although absolute attribution values shift slightly with the spatial representation, the relative attribution patterns remain stable. Moran’s eigenvectors showed a marginal advantage in local agreement, but the study’s central message is that spatial information, whatever its encoding, can be infused into machine learning models without distorting the resulting feature-importance hierarchy. Spatial block cross-validation, in which the grid was divided into four contiguous quadrants with one held out at each fold, further confirmed that testing R2 values remained high, generally between 0.82 and 0.92, suggesting the reported explanations were not artifacts of overfitting.

Sensitivity analysis under the nonlinear simulation scenarios showed only a modest decline in correspondence, with worst-case R2 values around 0.83 and best-case near 0.90 across 27 parameter combinations, implying the framework tolerates moderate departures from the linear assumptions under which it was benchmarked. The author cautions, however, that stronger nonlinearities, correlated predictors, and spatial confounding could reduce agreement further.

To demonstrate real-world applicability, the study revisited a ride-hailing demand dataset for Chicago comprising 795 census tract records, modeling the logarithm of trip counts with nine socioeconomic and network features. The XGBoost model reached a global R2 of 0.97, well above the 0.83 achieved by MGWR, and the SA-SHAP workflow produced contribution maps and binned contribution profiles that exposed clear spatial patterns. Educational attainment emerged as the dominant driver of ride-hailing trips at 27.7 percent of total contribution, followed closely by mean trip length at 25.8 percent, while street-network density contributed the least at 3.4 percent. Where MGWR agreed on the most and least influential features, discrepancies elsewhere were expected given the accuracy gap, and the author argues that when local regression performs poorly, a strong machine-learning model paired with SA-SHAP offers a compelling alternative for explanation.

The implications extend well beyond transportation research. Environmental science, climatology, urban planning, and the geosciences all depend on models whose predictions must be trusted by decision-makers, and the study suggests that spatially adjusted explanations can deliver transparency comparable to geographically weighted regression without sacrificing predictive power. The author also stresses what SA-SHAP is not: the interaction reallocation should not be read as causal inference, only as model-based attribution. Future work will push the framework toward gridded and point-based datasets at larger scales, uncertainty quantification of spatial explanations, and richer encodings such as graph-based or deep spatial embeddings. For now, the study offers spatial data scientists a practical recipe: let the machine learn the geography, then hand the geography back to the features that earned it. The complete code and data supporting the analysis have been released in a public GitHub repository, lowering the barrier for researchers eager to test whether their own black-box models can explain space as faithfully as the statisticians’ maps always have.