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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.30607 |
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| _version_ | 1866910271432294400 |
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| author | Davies, Tilman M. Desjardins, Michael R. Hohl, Alexander Wu, Guangzhen |
| author_facet | Davies, Tilman M. Desjardins, Michael R. Hohl, Alexander Wu, Guangzhen |
| contents | Distinguishing background heterogeneity from excess risk is a central challenge in case-control event data when both covariates and residual spatial or spatio-temporal structure matter. We develop a covariate-adjusted kernel regression framework that embeds an orthogonalized residual risk surface within a semiparametric binary model, and extend the approach from purely spatial to explicit spatio-temporal analysis. We apply the method to 959 gun violence incidents at public schools in the contiguous United States from 2000 to 2024, using incidents from the K-12 School Shooting Database linked to official school records for the corresponding year. The fitted models identify stable school-level associations, including markedly higher risk for larger schools and for middle and high schools, while also revealing substantial residual structure beyond the background distribution of schools. After adjustment for covariates, excess risk is found to remain concentrated in a persistent central-eastern corridor of the United States, with the strongest evidence appearing in recent years. More broadly, the analysis shows how residual risk surfaces can sharpen inference by separating background heterogeneity from anomalous structure in case-control event processes evolving over space and time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30607 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Orthogonalized Kernel Regression for Spatial and Spatio-Temporal Residual Risk: Application to School Shootings in the Contiguous United States Davies, Tilman M. Desjardins, Michael R. Hohl, Alexander Wu, Guangzhen Applications Methodology 62M30 Distinguishing background heterogeneity from excess risk is a central challenge in case-control event data when both covariates and residual spatial or spatio-temporal structure matter. We develop a covariate-adjusted kernel regression framework that embeds an orthogonalized residual risk surface within a semiparametric binary model, and extend the approach from purely spatial to explicit spatio-temporal analysis. We apply the method to 959 gun violence incidents at public schools in the contiguous United States from 2000 to 2024, using incidents from the K-12 School Shooting Database linked to official school records for the corresponding year. The fitted models identify stable school-level associations, including markedly higher risk for larger schools and for middle and high schools, while also revealing substantial residual structure beyond the background distribution of schools. After adjustment for covariates, excess risk is found to remain concentrated in a persistent central-eastern corridor of the United States, with the strongest evidence appearing in recent years. More broadly, the analysis shows how residual risk surfaces can sharpen inference by separating background heterogeneity from anomalous structure in case-control event processes evolving over space and time. |
| title | Orthogonalized Kernel Regression for Spatial and Spatio-Temporal Residual Risk: Application to School Shootings in the Contiguous United States |
| topic | Applications Methodology 62M30 |
| url | https://arxiv.org/abs/2605.30607 |