Statistics seminar - Associate Professor Tilman Davies - University of Otago

A seminar by Associate Professor Tilman Davies from University of Otago

Title: Orthogonalised Kernel Regression for Spatial and Spatio-temporal Residual Risk: Modelling School Shootings in the United States

Abstract: School gun violence in the United States is difficult to study nationally because the events are rare, varied, and not collected in a single official database. This talk presents a novel case-control formulation based on 959 public K–12 school gun-violence incidents in the contiguous United States from 2000–2024, linking incidents from the K–12 School Shooting Database to contemporaneous school-year records from the National Center for Education Statistics. Building on kernel-based case-control relative-risk regression, we use a semiparametric logistic model in which school-level predictors enter through a fixed-effects component and remaining structure is represented by a kernel-smoothed residual risk surface. The main methodological developments are an orthogonalised fitting scheme, which projects the smooth field away from the fixed-effects space, and an extension from spatial to spatio-temporal residual risk. Inference uses repeated control sampling (“bagging”), Monte Carlo reference fits, and exceedance contours. The fitted models identify stable school-level associations, especially higher incident odds for larger schools and for middle and high schools, and significant associations with demographic and socio-economic indicators. After adjustment for school characteristics and the background distribution of schools, residual risk remains geographically structured, with a central-eastern corridor of elevated spatial risk. A spatio-temporal extension shows that the strongest coherent excess is concentrated in recent years. We conclude by considering orthogonalised residual-risk surfaces as interpretable inferential objects in their own right, and by motivating our planned follow-up work on whether the detected residual elevations in incident risk are associated with broader state-level policy, firearm-law, and contextual environments.

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