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The authors have declared that no competing interests exist.

Little is known regarding the time trend of mass shootings and associated risk factors. In the current study, we intended to explore the time trend and relevant risk factors for mass shootings in the U.S. We attempted to identify factors associated with incidence rates of mass shootings at the population level. We evaluated if state-level gun ownership rate, serious mental illness rate, poverty percentage, and gun law permissiveness could predict the state-level mass shooting rate, using the Bayesian zero-inflated Poisson regression model. We also tested if the nationwide incidence rate of mass shootings increased over the past three decades using the non-homogenous Poisson regression model. We further examined if the frequency of online media coverage and online search interest levels correlated with the interval between two consecutive incidents. The results suggest an increasing trend of mass shooting incidences over time (p < 0.001). However, none of the state-level variables could predict the mass shooting rate. Interestingly, we have found inverse correlations between the interval between consecutive shootings and the frequency of on-line related reports as well as on-line search interests, respectively (p < 0.001). Therefore, our findings suggest that online media might correlate with the increasing incidence rate of mass shootings. Future research is warranted to continue monitoring if the incidence rates of mass shootings change with any population-level factors in order to inform us of possible prevention strategies.

Although mass shootings are rare violent behaviors compared with other violent crimes, these incidents adversely impact the society as a whole. A better understanding of risk factors associated with such violent behaviors could provide an initial key to possible intervention strategies. There have been only a handful of published studies that identified risk factors for mass shootings. The limited published findings may be, at least in part, attributable to their rarity that strains the analytic techniques. To partially circumvent this technical challenge, one may explore risk factors at the population level, which may shed some light on “points of prevention” from the perspective of public health. Therefore, we attempted to identify several population-level risk factors associated with such incidents in the current study.

The literature suggests several risk factors associated with homicides which may provide some clues to possible risk factors for mass shootings. Accumulating evidence suggested that gun ownership is associated with gun-related deaths. Although firearm-related murder rates are related to area-based gun ownership rate [

The limited understanding of mass shootings may have hindered the progress in dealing with this rising threat to the public health. We proposed to address three major questions in this study as follows. (1)

The definition of such an event is critical in the research on mass shootings. The definition of “mass shooting” is particularly critical in the current study since the rates of such an event is the key outcome. In our analyses, we defined a mass shooting as an act of firearm violence that resulted in at least four fatalities (not including the perpetrator), at the same time, or over a relatively short period of time in the case of shooting sprees. This definition is partially based on the definition of “mass murder” from a report of FBI’s Behavioral Analysis Unit [

The number of on-line reports about mass shootings were extracted using the Google searching engine. We used the “allintex” function in the Google search engine, and then specified the time frame using the function of “research tools” to calculate the number of on-line posted articles between two consecutive incidents. Briefly, we have used the following keywords: “mass shooting/shootings” or “rampage shooting/shootings” to extract all on-line public reports and posts that discussed mass shooting following a specific mass shooting event. The media coverage density (i.e., daily number of online reports and posts) was then calculated as the number of on-line articles divided by the length of the period between the relevant incident and the next incident. Previous studies have shown that the Google searching engine can effectively retrieve the information about the impact of the media [

To investigate the impact of state-level gun ownership rate on the mass shooting rate, we built a Poisson model for state-specific incidence count with other covariate effects such as state specific serious mental illness rate and poverty percentage, and population size as an offset variable in a Bayesian framework, with two random effects for structured and unstructured spatial correlation structure. Since there were no mass shooting incidents in 19 states during this period of 32 years, we used zero-inflated Poisson count model to adjust for the excessive zeroes. All incidents were summarized by state as counts, regressed on gun ownership rate through a log-link function as,
_{i} is structured random state effect with an intrinsic conditional autoregressive (CAR) model was specified as a prior distribution, and _{i} is unstructured random effect with an exchangeable normal distribution with zero mean as a prior distribution. The use of spatial model, specifically the CAR model was intended to adjust for the effect for similar neighborhood characteristics among the states sharing common borders. This model can examine not only the state’s mass shooting rate but also the corresponding rates in all surrounding states. Therefore, spatial modeling could enhance both the estimates and our knowledge of the degree of uncertainty associated with these estimates, and may overcome the effect of artificial state boundaries. The model for the excess zeroes considers the same predictors as the main Poisson model. In addition, we also treated the logarithms of state-specific population size as an offset, instead of a covariate, to examine the relationship between covariates and probability of shootings.

To evaluate if the incidence rate was increasing during the past three decades, we implemented a non-homogenous Poisson regression model on biannual incidence count for the U.S. with a linear

We further investigated the speculated relationship between mass shootings and two online media indexes: (1) online media coverage and (2) online search interest. We hypothesize that the higher online media coverage density (i.e., the frequency of online media attention to the theme of “mass shootings” in a certain period of time) after a particular shooting might be associated with the shorter interval between this incident and the next one. We, therefore, calculated the online media coverage density by calculating the daily number of reports and posts about mass shootings during the interval between two consecutive incidents to investigate if media attention between an earlier shooting event could correlate with “when” the next shooting might occur. To alleviate the confounding effect due to the time trend that Google became the dominating Internet searching service provider in the late 2004, we only analyzed a subset of mass shooting incidents in our data set that occurred between January of 2005 and May of 2018. The distributions of media coverage density were highly skewed. Hence, we log-transformed the variable of media coverage density before we performed the Poisson regression model to see if the between-incident interval could be predicted by media coverage density adjusting for number of fatalities and the number of injuries, with time as an offset. Similarly, we tested if the same outcome could be predicted by the level of Internet search interest. Finally, we evaluated the associations between the outcome and both online media coverage density and search interest levels by adjusting the numbers of fatalities and injuries in the same Poisson model.

There was a total of 100 mass shootings in the U.S. recorded in our compilation of data from January 1982 to May 2018, with 833 fatalities, and 1,292 injuries. The spatial locations of the shootings in the 48 states are displayed in

Parameter | Mean | SD | 2.5% Percentile | Median | 97.5% Percentile |
---|---|---|---|---|---|

Intercept | -1.23 | 2.99 | -6.9 | -1.49 | 5.06 |

FS/S |
-0.35 | 1.24 | -2.82 | -0.35 | 2.19 |

Serious mental disorder rate | 0.02 | 0.15 | -0.29 | 0.04 | 0.29 |

Poverty rate | -0.02 | 0.05 | -0.07 | 0.018 | 0.13 |

Gun law permissiveness | -0.26 | 0.39 | -1.06 | -0.25 | 0.49 |

* FS/S denotes the ratio of firearm-related suicides divided by all suicides.

The two Poisson regression models that examined the incidence rate show that the frequency of mass shootings has been increasing in recent three decades (p-value < 0.001). According to the AIC level, the model that focused on the biannual incidence rate may have a better goodness of fit than the model that focused on annual incidence rate (AIC levels were 93 and 122, respectively). The biannual incidence rates are shown in the

To model the temporal trend for incidence rates, we adjusted the model with a time-varying Poisson process, i.e. a non-constant rate

According to the Poisson model, the possible over-dispersion parameter was estimated to be 1.53, which indicates a moderate effect. If the current frequency trend continues, we can assess the risk by adopting the monthly intensity rate from the above non-homogeneous Poisson model for the most recent year, ^{rd} column of

Within months ( |
Probability of a shooting 1 − ^{−0.227t} |
Probability of a shooting 1 − ^{−0.468t} |
---|---|---|

1 | 0.203 | 0.374 |

2 | 0.366 | 0.608 |

3 | 0.494 | 0.755 |

6 | 0.745 | 0.940 |

9 | 0.871 | 0.985 |

12 | 0.935 | 0.996 |

In an attempt to explain this time trend, we performed a pair-wise correlation analysis of online media coverage, online search interest levels, and mass shootings. The correlation analysis results are summarized in

Our study has attempted to answer three important questions concerning population-level risk factors associated with mass shootings, increasing rate of mass shooting, and the contagious effect. The results suggest that the neither proportion of suicides by firearms (as a proxy for gun ownership), poverty rate, nor serious mental illness rate, could significantly predict the state-specific mass shooting rate. However, the both annual and bi-annual incidence rates of mass shootings in the U.S. have been found to steadily increased during the past 30 years. We further observed that increasing online media attention is correlated with decreasing intervals between shooting incidents–which might be considered to lend some support to the hypothesis of a “contagious effect”.

Both gun ownership and the rate of mass shootings declined simultaneously in Australia during 1979–2013 [

Our data suggest that the state-level rate of serious mental illness could not predict the mass shooting rate. There is evidence for an increased prevalence and severity of mental illness in adults in recent years [

Our results suggest that the on-line media coverage of the current shootings as well as internet search interest levels may predict how soon the next shooting tragedy may occur. The positive correlation between on-line media coverage and search interest might provide some clues to the predisposing factors underlying the contagion effect. However, our estimates based on the population-level data may not reflect the genuine influence of media exposure on individuals. With the growing popularity of social networking on-line media, the media exposure to mass shootings solely based on the internet-based reports may underestimate the total level of relevant media exposure since most of the social networking media-related activities cannot be directly accessed through on-line data queries. Although we cannot rule out some confounders for the relationship between media coverage and the rising incidence of mass shootings, media exposure seems to play a role. There have been several recent studies using Google to study social behaviors–three have been focused on violent behaviors [

Our media-related analysis has several limitations. First, we only focused on the most proximal preceding incident, and hence we ignored the impact of media coverage on more distant incidents. Although the media coverage on cumulative mass shooting incidents is overall greater at more recent time-points, compared to earlier incidents, we could not rule out the confounding effect of some incidents that generated more media attention despite being temporally more distant. This confounding effect, if present, would by default make more recent incidents subject to higher levels of accumulative influence of media. We have adjusted for the temporal order and found the effect of media coverage remained significant. Meanwhile, we also examined the role of on-line search interest levels in the incidence of mass shootings. On-line search interest did positively correlate with on-line media coverage. Therefore, we might infer that the frequency of on-line related reports might reflect both interest levels of the media providers and consumers, and vice versa. Second, we calculated the media coverage by counting the number of on-line reports. However, the emergence of social networking web resources may play a role in the time-dependent increment of media exposure to these incidents; such a confounding effect of social networking could not be measured with the current analytic methods. Similarly, the internet search interest levels could not capture the interest levels of consumers in the social media. Although on-line news reports and articles only represent a fraction of media exposure related to mass shootings, on-line articles, especially those related to social networking (e.g., Twitter), may correlate with other types of media coverage, such as television [

Recent evidence suggests a “contagion” in mass shootings–which refers to the phenomenon that a mass shooting may temporarily increase the probability of a similar event in the immediate future [

To further examine if some specific shootings that receive unusually high media attention are outliers that bias the observation, we have also examined the post-event effects for three specific incidents: the mass shooting at Sandy Hook Elementary School in December of 2012, the mass shooting at Las Vegard strip October of 2017, and the mass shooting at Marjory Stoneman Douglas High School shooting in February of 2018. The first case triggered the presidential initiative of firearm regulation reform proposals; the second case caused the largest number of fatalities associated with mass shooting in the history of the U.S.A.; the third case triggered the largest nationwide protest that called for firearm regulation reforms. We found that the media index values, such as number of daily online articles and the online search interest level, were increased variably (Sandy Hook Elementary School shooting 3%, Las Vegard strip shooting 14%, and Marjory Stoneman Douglas High School shooting 241%). The second case caused increased media attention, and the interval between this case and its following shooting incident was 17 days, which was 0.7 standard deviation below the mean of the distribution of the log-transformed intervals. The third case apparently caused unusually heightened media attention, and the interval between the third case and its following shooting incident was 23 days, which was 0.5 standard deviation below the mean of the distribution of the log-transformed intervals. Therefore, these particular observations seemed to follow the trend that media attention was inversely correlated with the interval between the current shooting event and the next shooting event, especially for the more recent cases. Furthermore, we removed these “outliers” and re-ran the analysis. The results still show that higher internet media exposure was significantly correlated with a shorter interval between the corresponding shooting and the following shooting. Therefore, the original observations were not biased by the “outliers” that triggered unusually high media attention levels.

Another limitation lies in the assumptions in the process of statistical modeling. For example, we relied on the cross-sectional data to evaluate ownership rates, wherein a spatial correlation structure is needed with priors specified from a Bayesian analysis. Our statistical approaches were hence different from Wallace’s methods in a recent study, and hence we did not replicate the prior findings that gun ownership could account for the incidence of mass shootings [

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