Network analysis of rearm movement among US states

Background: The movement of rearm across state lines may decrease the effectiveness of state-level rearm laws. Yet how state-level rearm policies affect cross-state movement have not yet been widely explored. This study aims to characterize the interstate movement of rearms and its relationship with state-level rearm policies. Methods : Cross-sectional time series network analysis of interstate rearm movement using Bureau of Alcohol, Tobacco, Firearms, and Explosives rearm trace data (2010 -2017). We constructed the network of rearm movement between 50 states. We used zero-inated negative binomial regression to estimate the relationship between the number of a state’s rearm laws and number of states for which it was the source of 100 or more rearms, adjusting for state characteristics. We used a similar model to examine the relationship between rearm laws and the number of states for which a given state was the destination of 100 or more rearms. Results : Over the 8-year period, states had an average of 26 (SD 25.2) rearm laws. On average, a state was the source of 100 or more crime-related rearms for 2.2 (SD 2.7) states and was the destination of 100 or more crime-related rearms for 2.2 (SD 3.4) states. Greater number of rearm laws was associated with states being the source of 100 or more rearms to fewer states (IRR0.67 per SD, p<0.001), higher odds of not being a source to any states (aOR1.56 per SD, p<0.001), and states being the destination of 100 or more rearms from more states (IRR1.83 per SD, p<0.001). Conclusions: Restrictive rearm policies are associated with less other states, but with The rearm-restricting by a of interstate


Background
Studies on rearm laws and rearm-related violence have focused on the association between the rates of rearm-related violence within the state and the aggregate number (1) or categories of state-level rearm laws (2)(3)(4)(5)(6). A recent systematic review found that stronger state-level rearm laws are associated with reductions in rearm-related homicide rates; however, it also found inconclusive and con icting results for many of the different categories of laws (7).
The extent to which states can regulate rearm-related violence with state-level rearm laws depends on their ability to regulate the rearms within their borders. However, rearms move across state borders (8,9), and this movement may be due in part to the rearm laws themselves. For example, the implementation of a law limiting handgun purchases in Virginia resulted in a lower proportion of crimerelated rearms recovered in the entire Northeast region that were traced to Virginia (10). States with more stringent rearm laws in general have a higher proportion of crime-related rearms originating from outside the state (8,11), of which a large proportion are from states with weaker rearm laws (12). For pairs of states, increasing rearm law stringency in the source state was associated with reduced movement of rearms between two states, while increasing stringency in the destination state lead to increased movement (9,13).
This study aims to build upon the literature on interstate rearm movement by describing a network analysis to assess crime-related rearm movement between states over an eight-year period. Prior studies have relied on measuring the proportions of rearms originating from source states, or the relative differences in state-level rearm laws between two states and the movement of rearms between them.
However, this has a limited ability to examine the dynamic interplay of what is happening between all states and within each state at the same time. The network approach allows us to examine the relationships among all states simultaneously and study the movement of rearms both into and out of each state. We hypothesize that states with fewer rearm laws serve as source states of crime-related rearms recovered in other states, and that states with more rearm laws serve as destination states of crime-related rearms from other states.

Study Design and Data Source
This is a cross-sectional time series analysis of state-level data from 2010 to 2017. The study was determined to be exempt from Institutional Review Board regulation at the University of California, Los Angeles because it uses de-identi ed, publicly available, state-level data.

Network of rearm movement:
We constructed the network of rearm movement between 50 states using publicly available rearm trace data (2010-2017) from the Bureau of Alcohol, Tobacco, Firearms, and Explosives (ATF) at the time this study was conducted. The ATF maintains a database of rearms used in crimes which are successfully traced to their original point of purchase (14). The ATF conducts rearm tracing at the request of law enforcement agencies engaged in a criminal investigation where a rearm has been used or is suspected to have been used in a crime, with the intent to provide investigative leads to law enforcement to linking a suspect to a rearm in the criminal investigation and to identify trends and pattens in the movement of illegal rearms. Using these data, we de ned a network tie between 2 states when there was movement of 100 or more rearms in a given year from the state where the rearm is purchased ("source state") to the state where the rearm is recovered ("destination state"). A state could serve as both a source state and a destination state for another state if it was both a source and destination for 100 or more rearms in a given year. A network of rearm movement was constructed for each year, for a total of 8 networks. For each state, we calculated the number of states for which it served as source state (outdegree) and the number of states for which it served as destination state (indegree). Sensitivity analyses were conducted by constructing the network of rearm movement using the cut-off of 50 or more rearms.

Dependent Variables:
The primary dependent variables were the number of states for which the index state was the source of 100 or more crime-related rearms in a given year (outdegree) and the number of states for which the index state was the destination of 100 or more crime-related rearms in a given year (indegree), which were calculated based on the network described above.

Independent Variables:
Following other studies (1,11,15), the independent variable was the rearm law strength score, an unweighted count of state-level rearm laws. This variable was obtained from the State Firearm Laws Database, which compiles data on state-level laws in all 50 states since 1991 and codes them into fourteen categories of laws that regulate and deregulate rearms (16). Laws regulating rearms include those regulating dealers and buyers, those regulating possession of rearms, those regulating purchase or possession of assault weapons, and those preventing individuals with a history of crime, domestic violence, and mental health conditions from possessing rearms. Laws deregulating rearms include laws providing blanket immunity to rearm manufacturers and Stand-Your-Ground laws that allow individuals to use rearms with immunity from the law when they can claim a self-de ned need to protect their property. A higher rearm-law strength score denotes more laws regulating rearms and fewer laws deregulating rearms. This variable was scaled to have a mean of 0 and a standard deviation of 1. We examined all state-level rearm laws rather than limiting the focus to those that speci cally prohibit rearm tra cking through regulation of purchase of rearms with the intent to resell or purchase on behalf of another person. Prior studies have found that numerous categories of state-level rearm laws, ranging from those that regulate purchase or registration of rearms, those that regulate concealed carry permits, to those that allow municipalities and cites to regulate rearms, were associated with less interstate movement of crime-related rearms (9,10,17,18). Further, studies interviewing persons incarcerated for rearm-related offenses showed that the majority of rearms were acquired through their friends, acquaintances, family members, and other members of their social network (19,20). Such transactions in the secondary rearm market were unreported and remained unregulated by laws targeting rearm tra cking, especially as many laws exempt the transfer or sale of the rearm to relatives.

Covariates:
We used the following state-level data to adjust for characteristics previously associated with rearmrelated violence: poverty rate (21,22), a validated proxy measure for state-level rearm ownership (23), and county-weighted state density as a proxy for the average urbanicity of the state (the sum across all counties in the state of [county population / county land area] * [county population / state population]) (21,24). The proxy measure of state-level rearm ownership developed by Siegel and colleagues (23) uses the proportion of rearm suicides in a state and per capita number of hunting licenses, and is highly correlated with survey-measured, household rearm ownership at 0.95. We also adjusted for state area and census division to account for differences in rearm movement by state size and geographic location. These variables were scaled to have a mean of 0 and a standard deviation of 1.

Data Analysis:
The distribution of the number of states for which the index state serves as the origin or destination of 100 or more crime-related rearms is skewed to the right and contains a large proportion of zeros. Therefore, we tted zero-in ated negative-binomial models, which is designed to address overdispersion and excess zeros when analyzing count data. A Poisson model assumes that the conditional mean is equal to the conditional variance. Negative binomial models are modi ed Poisson regression models that relax this assumption, allowing the conditional mean and variance to be estimated separately. Zero-in ated models assume that there are two latent groups: observations that necessarily have a high probability of a zero outcome because of some underlying attributes (there are referred to in the literature as excess zeros), and observations that might have a zero, but might have a positive count with nonzero probability (25). In the context here, rearm movement, say, from Alaska to Florida is likely to be an excess zero because of the distance involved, while movement from Georgia to Florida is likely to be driven by policy differences. Zero-in ated models are two-part models which consist of a binary model and count model (in our case, negative binomial model) to account for excess zero (26). We tted a xed-effects zero-in ated negative-binomial model to estimate the association between the number of rearm laws and the number of states for which the index state serves as destination of 100 or more crime-related rearms in a given year, adjusting for the covariates listed above. We subsequently tted zero-in ated negative-binomial regression models to estimate the association between the number of states for which the index state is the source of 100 or more crime-related rearms in a given year, adjusting for covariates. A Vuong non-nested test was used to determine whether the zero-in ated negative-binomial model had a better t than a negative-binomial model without zeroin ation. Sensitivity analyses were conducted by tting similar models but using the cut-off of 50 or more rearms. The networks were constructed and analyzed using igraph version 1.2.4.1 and sna version 2.4 packages for R. Zero-in ated negative-binomial regression with robust con dence intervals were conducted using Stata version 16. Table 1 presents the results of descriptive characteristics. States had an average of 26 (SD 25.2) rearm laws, ranging from two laws (Idaho, Mississippi and Missouri in 2017) to 106 laws (California in 2017) ( Figure 1). On average, a state was the source of 100 or more crime-related rearms for 2.2 (SD 2.7) states. This ranged from Texas in 2017, which was the source of 100 or more crime-related rearms to 15 states, to 142 observations over eight years (36%) in which a state was the source of 100 or more crimerelated rearms to zero other states that year. On average, a state was the destination of 100 or more crime-related rearms for 2.2 (SD 3.4) states. This ranged from California in 2017, which was the destination for 100 or more crime-related rearms from 22 states, to 181 observations (45%) over eight years in which a state was the destination of 100 or more crime-related rearms from zero states that

Results
year.
The network of interstate rearm movement is depicted in Figure 2, which shows the average movement of rearms across states over 8 years, when the average is 100 or more rearms. The width of the arrow between two states is proportional to the average number of rearm movement between those states. States that do not have an average of 100 or more rearms move across its borders are excluded from this gure, as are New Hampshire and Massachusetts, which are connected to each other but not to other states. California (120 rearms). The general pattern evoked by Figure 2 is of gun ows from low-regulation states in the south and southwest to high-regulation states. Table 2 presents the results of the multivariable zero-in ated negative binomial analysis estimating the relationship between rearm laws in a state and the number of states for which it serves as the source of 100 or more crime-related rearms. Each additional standard deviation in the number of rearm laws was associated with 33% fewer states to which a given state is the source of 100 or more crime-related rearms incidence rate ratio (IRR) = 0.67 (b = -0.40, 95% con dence interval Multivariable zero-in ated negative-binomial analysis estimating the relationship between rearm laws and the number of states to which a state is the destination of 100 or more crime-related rearms is shown in Table 3. Each additional standard deviation in the number of rearm laws in a state is associated with 83% more states for which it is the destination of 100 or more crime-related rearms (IRR = 1.83; b = -0.60, 95% CI 0.47, 0.74, p <0.001), adjusting for covariates. The Vuong test of zero-in ated negative binomial model versus negative binomial showed that V = 4.78 (p<0.001), rejecting the negative binomial model in favor of the zero-in ated negative-binomial model.
Sensitivity analyses using the cut-off of 50 rearms instead of 100 showed similar results (Appendix Tables 1 and 2). Each additional standard deviation in the number of rearm laws is associated with higher odds of not being the source of 50 or more crime-related rearms to any state (aOR =

Discussion
Using longitudinal data on crime-related rearm tracing and state-level rearm laws, we constructed a network of rearm movement across US states from 2010 -2017, demonstrating associations between state-level rearm policy and movement of rearms into and out of states. Consistent with our hypothesis, more rearm laws in a state was associated with both it being the source of crime-related rearms to fewer states, and the destination of crime-related rearms from more states. The estimated associations were statistically signi cant, robust to the inclusion of multiple covariates including statelevel poverty, density, and a rearm ownership proxy.
Our ndings corroborate earlier studies showing that a passage of a single law in one state can impact the movement of rearms into and out of the state. After the implementation of a one handgun per month law in Virginia in 1993, the crime-related rearms recovered in a Northeast state was less likely to be traced to Virginia compared to other Southeast states (10). Similarly, after the passage of Brady Bill, which instituted mandatory background checks, there was a large reduction in rearms recovered in Chicago originating from states that were not conducting background checks prior to the Brady Bill (27). Studies among incarcerated people have found that crime-related rearms are often obtained in illegal secondary markets composed of social network members (19,20). Our study suggests that increasing rearm laws may decrease rearms that are available for transfer in the illegal rearm market.
Further, we found that more rearm laws was associated with a state being the destination of 100 or more crime-related rearms from more states. This is consistent with studies examining pairs of states that showed the differential in rearm laws between source and destination states correlated with the movement of rearms between the two states, such that rearms are more likely to move from states with weaker laws to states with stricter laws (9,13). Similarly, a study of 25 US cities found that cities in states with mandatory registration and licensing systems had a higher proportion of crime-related rearms originating from other states (8), and that states with higher number of rearm laws had a higher percentage of crime-related rearms originating from other states (11).
We also found that the rearm ownership in a given state was associated with both having fewer states for which it is a source of rearms and having higher odds of not being a destination of rearms from other states, after adjusting for the number of rearm laws and covariates. Recent studies have begun to examine the independent effects of state-level rearm laws and rearm ownership on rearm-related outcomes. A study showed an additive relationship between them, in which state-level rearm permissiveness and rearm ownership were both associated with a higher rate of mass shootings (28), while another study showed a moderating relationship in which state-level rearm policy strength was inversely associated with suicide rates in states with higher levels of rearm ownership (29).

Conclusion Strengths and Limitations
Interpretation of our ndings are subject to limitations. This is an associative study, and as such we are unable to establish causality between rearm laws and movement of crime-related rearms. Our gun ownership variable was a proxy measure and we did not have detailed data on actual gun ownership at the state level. As an ecological analysis, the study cannot make any causal claims at the individual level, but instead points to policy factors associated with state-level rearm movement. The rearm trace data used in our analysis only included rearms used in crimes that were recovered by law enforcement, not all rearms or all rearms used in crimes. Finally, this study did not assess the impact of interstate rearm movement on negating the effects of stricter rearm laws, nor how such a relationship could affect overall state rates of rearm-related violence. These issues should be explored in future research studies as it is possible that the relationships identi ed in this study in uence overall rates of rearm-related violence. Strengths of the study include using longitudinal data over an eight-year period and including all 50 states to give a more complete picture of how rearms are shared among states.
Taken together, these results suggest that the effectiveness of rearm-restricting policies at the state level is complicated by a network of rearm movement among states. These results suggest that rearms travel in complicated webs among states, and that therefore state-level rearm policies may not su ciently address rearm availability within states. This may in part explain why certain rearm laws have not been found to have the intended effects on rearm-related violence: a recent systematic review showed that state-level laws that aim to curb rearm tra cking through regulating rearm dealers and mandating theft reporting showed con icting and inconclusive results on the state's rearm-related violence (7). Our study suggests the need for federal or regional rearm laws that may better regulate crime-related rearms that move across states.

Declarations
Consent for publication: All authors of the manuscript have read and agreed to its content and are accountable for all aspects of the accuracy and integrity of the manuscript in accordance with ICMJE criteria. The article is original, has not already been published in a journal, and is not currently under consideration by another journal. We agree to the terms of the BioMed Central Copyright and License Agreement.   Zero-in ation model