Estimating effects within nonlinear autoregressive models: a case study on the impact of child access prevention laws on firearm mortality

TL;DR

This paper develops a method for interpreting effects of interventions in nonlinear autoregressive models, specifically negative binomial models, and applies it to assess the impact of child access prevention laws on firearm mortality in the US.

Contribution

It introduces a simple approximation for interpreting autoregressive model parameters in nonlinear count data models, demonstrated through a case study on firearm mortality.

Findings

Child access prevention laws reduce firearm mortality.

The proposed method allows clear interpretation of intervention effects.

Application to 36 years of US data shows policy impact.

Abstract

Autoregressive models are widely used for the analysis of time-series data, but they remain underutilized when estimating effects of interventions. This is in part due to endogeneity of the lagged outcome with any intervention of interest, which creates difficulty interpreting model coefficients. These problems are only exacerbated in nonlinear or nonadditive models that are common when studying crime, mortality, or disease. In this paper, we explore the use of negative binomial autoregressive models when estimating the effects of interventions on count data. We derive a simple approximation that facilitates direct interpretation of model parameters under any order autoregressive model. We illustrate the approach using an empirical simulation study using 36 years of state-level firearm mortality data from the United States and use the approach to estimate the effect of child access prevention laws on firearm mortality.