A Bayesian Model of Underreporting for Sexual Assault on College Campuses

TL;DR

This paper develops a hierarchical Bayesian model to estimate true sexual assault incidence and reporting rates on college campuses, revealing significant variation in underreporting and increasing reporting trends over time.

Contribution

It introduces a Bayesian approach with informative priors and HMC sampling to disentangle true assault numbers from underreporting at individual schools.

Findings

Reporting rates increased from 2014 to 2019

Significant variation in underreporting across schools

Implications for interpreting campus crime statistics

Abstract

In an effort to quantify and combat sexual assault, US colleges and universities are required to disclose the number of reported sexual assaults on their campuses each year. However, many instances of sexual assault are never reported to authorities, and consequently the number of reported assaults does not fully reflect the true total number of assaults that occurred; the reported values could arise from many combinations of reporting rate and true incidence. In this paper we estimate these underlying quantities via a hierarchical Bayesian model of the reported number of assaults. We use informative priors, based on national crime statistics, to act as a tiebreaker to help distinguish between reporting rates and incidence. We outline a Hamiltonian Monte Carlo (HMC) sampling scheme for posterior inference regarding reporting rates and assault incidence at each school, and apply this method to campus sexual assault data from 2014-2019. Results suggest an increasing trend in reporting rates for the overall college population during this time. However, the extent of underreporting varies widely across schools. That variation has implications for how individual schools should interpret their reported crime statistics.