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  1. Abstract

    Claiming causal inferences in network settings necessitates careful consideration of the often complex dependency between outcomes for actors. Of particular importance are treatment spillover or outcome interference effects. We consider causal inference when the actors are connected via an underlying network structure. Our key contribution is a model for causality when the underlying network is endogenous; where the ties between actors and the actor covariates are statistically dependent. We develop a joint model for the relational and covariate generating process that avoids restrictive separability and fixed network assumptions, as these rarely hold in realistic social settings. While our framework can be used with general models, we develop the highly expressive class of Exponential-family Random Network models (ERNM) of which Markov random fields and Exponential-family Random Graph models are special cases. We present potential outcome-based inference within a Bayesian framework and propose a modification to the exchange algorithm to allow for sampling from ERNM posteriors. We present results of a simulation study demonstrating the validity of the approach. Finally, we demonstrate the value of the framework in a case study of smoking in the context of adolescent friendship networks.

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  2. Context

    US states are largely responsible for the regulation of firearms within their borders. Each state has developed a different legal environment with regard to firearms based on different values and beliefs of citizens, legislators, governors, and other stakeholders. Predicting the types of firearm laws that states may adopt is therefore challenging.


    We propose a parsimonious model for this complex process and provide credible predictions of state firearm laws by estimating the likelihood they will be passed in the future. We employ a temporal exponential‐family random graph model to capture the bipartite state law–state network data over time, allowing for complex interdependencies and their temporal evolution. Using data on all state firearm laws over the period 1979–2020, we estimate these models’ parameters while controlling for factors associated with firearm law adoption, including internal and external state characteristics. Predictions of future firearm law passage are then calculated based on a number of scenarios to assess the effects of a given type of firearm law being passed in the future by a given state.


    Results show that a set of internal state factors are important predictors of firearm law adoption, but the actions of neighboring states may be just as important. Analysis of scenarios provide insights into the mechanics of how adoption of laws by specific states (or groups of states) may perturb the rest of the network structure and alter the likelihood that new laws would become more (or less) likely to continue to diffuse to other states.


    The methods used here outperform standard approaches for policy diffusion studies and afford predictions that are superior to those of an ensemble of machine learning tools. The proposed framework could have applications for the study of policy diffusion in other domains.

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