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Over the last fifty years, the United States have experienced hundreds ofmass public shootings that resulted in thousands of victims. Characterized bytheir frequent occurrence and devastating nature, mass shootings have become amajor public health hazard that dramatically impact safety and well-being ofindividuals and communities. Given the epidemic traits of this phenomenon,there have been concerted efforts to understand the root causes that lead topublic mass shootings in order to implement effective prevention strategies. Wepropose a quantile mixed graphical model for investigating the intricacies ofinter- and infra-domain relationships of this complex phenomenon, whereconditional relations between discrete and continuous variables are modeledwithout stringent distributional assumptions using Parzen's definition ofmid-quantile. To retrieve the graph structure and recover only the mostrelevant connections, we consider the neighborhood selection approach in whichconditional mid-quantiles of each variable in the network are modeled as asparse function of all others. We propose a two-step procedure to estimate thegraph where, in the first step, conditional mid-probabilities are obtainedsemi-parametrically and, in the second step, the model parameters are estimatedby solving an implicit equation with a LASSO penalty.

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