Modeling Perpetrators' Fate-to-Fate Contagion in Public Mass Shootings In The United States Using Bivariate Hawkes Processes

TL;DR

This paper models how the outcome of perpetrators in mass shootings influences subsequent incidents using bivariate Hawkes processes, revealing significant cross-contagion effects and timescales for different event types.

Contribution

It introduces a novel application of bivariate Hawkes processes to quantify the contagion effects between different perpetrator fates in mass shootings.

Findings

Strong spillover from 'live' to 'die at the scene' incidents with a 20-day contagion timescale.

No significant reverse influence from 'die at the scene' to 'live' incidents.

Self-excitation observed only within the same event type, with a 20-hour timescale.

Abstract

This study examines how the fate of a perpetrator in a public mass shooting influences the fate of subsequent perpetrators. Using data from 1966 to 2024, we classify incidents according to whether the perpetrator died at the scene or survived the attack. Using a bivariate Hawkes process, we quantify the cross-excitation effect, which is the triggering effect that each event type exerts on the other, i.e., "die at the scene"$\rightarrow$ "live" and "live"$\rightarrow$ "die at the scene", as well as the self-excitation effects, i.e., "die at the scene"$\rightarrow$ "die at the scene" and "live"$\rightarrow$ "live". Our results show that the strongest spillover was from "live" incidents to "die at the scene", where we estimate that 0.34 (0.09, 0.80) of "die at the scene" incidents are triggered by a prior event in which the offender survived the attack. This pathway also exhibits the longest estimated contagion timescale: approximately 20 days. In contrast, the reverse influence, that is, "die at the scene"$\rightarrow$"live", is not statistically significant, with the lower bound of its 95% confidence interval nearly equal to zero. We also find that "die at the scene" events can only cause their own type, where 0.139 (0.01, 0.52) of such incidents are caused by previous "die at the scene" events, with the shortest contagion timescale of roughly 20 hours.