From Regression Analysis to Deep Learning: Development of Improved Proxy Measures of State-Level Household Gun Ownership

In the absence of direct measurements of state-level household gun ownership (GO), the quality and accuracy of proxy measures for this variable are essential for firearm-related research and policy development. In this work, we develop two highly accurate proxy measures of GO using traditional regression analysis and deep learning, the former accounting for non-linearities in the covariates (portion of suicides committed with a firearm [FS/S] and hunting license rates) and their statistical interactions. We subject the proxies to extensive model diagnostics and validation. Both our regression-based and deep-learning proxy measures provide highly accurate models of GO with training R(2) of 96% and 98%, respectively, along with other desirable qualities—stark improvements over the prevalent FS/S proxy (R(2) = 0.68). Model diagnostics reveal this widely used FS/S proxy is highly biased and inadequate; we recommend that it no longer be used to represent state-level household gun ownership in firearm-related studies.