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Spatial outliers as a pattern determinant for explaining heterogeneity
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DOI：10.1080/13658816.2026.2682957.png)
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Abstract
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Explaining spatial heterogeneity typically relies on first-dimension covariates that describe spatial gradients. However, many geographic phenomena also exhibit irregular and locally extreme structures that are difficult to capture using smooth relationships. This study proposed a second-dimension outlier-driven heterogeneity (SOH) model, in which the first dimension refers to covariate variation across space, while the second dimension represents spatial pattern information captured from local outlier configurations. SOH derives multi-scale spatial outlier patterns (SOPs) using a second-dimension outlier model and embeds them in a stratification-detection workflow, where decision tree-based stratification defines strata and the geographical detector evaluates explanatory power via the power of determinant (PD). The model supports evaluation of individual effects, SOP interactions, and SOP-variable interactions, with assessment of scale dependence across neighbourhood buffers. Application of this model to spatial heterogeneity in Australian barley production showed that SOPs strengthened heterogeneity explanation relative to original variables, and that SOP interactions and SOP-variable interactions yielded synergistic gains in PD. A scale threshold around 200 km was identified, beyond which SOP-only models approached the explanatory performance of combined models, indicating that multi-scale SOPs captured broad spatial context. Overall, SOH provides a unified approach for incorporating outlier-driven spatial patterns into spatial heterogeneity analysis.
Keywords:
Spatial heterogeneity
spatial outlier patterns
second-dimension outliers
geographical detector
stratification-based analysis
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