Logistic Regression for Extremely Rare Events: The Case of School Shootings

Abstract

School shootings are often used in public policy debate as a justification for increased regulation, based on qualitative arguments. However, to date, no effort has been made to find valid quantitative evidence for the claims bolstering the regulation recommendations. In defense of this absence of evidence, it is usually argued that the rarity of such events does not allow the employment of quantitative methods. This paper, using a simulation study, shows that, based on the number of school shootings in the United States and Germany combined, the well-known method of logistic regression can be applied to a case-control study, making it possible to at least test for an association between hypothesized influential variables and the occurrences. Moderate relative risks, explained by an observed variable, would lead to a high power of the appropriate test. A moderate numbers of cases generated by such a variable would suffice to show a significant association.

Keywords: Rare Events, Logistic Regression, Case-Control Studies, School Shootings

JEL Classification: C25, C35, I18, K14