Quantile mixed graphical models with an application to mass public shootings in the United States

TL;DR

This paper introduces a novel quantile mixed graphical model to analyze complex relationships between variables related to mass public shootings in the US, aiming to improve understanding and prevention strategies.

Contribution

It develops a new statistical modeling approach that captures intricate variable relationships without strict distributional assumptions, specifically applied to mass shooting data.

Findings

Identifies key variable connections in mass shooting data

Provides a sparse, interpretable network structure

Demonstrates effectiveness of the model in real data analysis

Abstract

Over the last fifty years, the United States have experienced hundreds of mass public shootings that resulted in thousands of victims. Characterized by their frequent occurrence and devastating nature, mass shootings have become a major public health hazard that dramatically impact safety and well-being of individuals and communities. Given the epidemic traits of this phenomenon, there have been concerted efforts to understand the root causes that lead to public mass shootings in order to implement effective prevention strategies. We propose a quantile mixed graphical model for investigating the intricacies of inter- and infra-domain relationships of this complex phenomenon, where conditional relations between discrete and continuous variables are modeled without stringent distributional assumptions using Parzen's definition of mid-quantile. To retrieve the graph structure and recover only the most relevant connections, we consider the neighborhood selection approach in which conditional mid-quantiles of each variable in the network are modeled as a sparse function of all others. We propose a two-step procedure to estimate the graph where, in the first step, conditional mid-probabilities are obtained semi-parametrically and, in the second step, the model parameters are estimated by solving an implicit equation with a LASSO penalty.