# Extremist ideology as a complex contagion: the spread of far-right radicalization in the United States between 2005 and 2017

## Introduction

The far-right movement, which includes white supremacists, neo-Nazis, and sovereign citizens, is the oldest and most deadly form of domestic extremism in the United States (Piazza, 2017; Simi and Bubolz, 2017). Despite some ideological diversity, members of the far-right often advocate for the use of violence to bring about an “idealized future favoring a particular group, whether this group identity is racial, pseudo-national, or characterized by individualistic traits” (National Consortium for the Study of Terrorism and Responses to Terrorism (START), University of Maryland, 2017). Over the last decade, the far-right movement was responsible for 73.3% of all extremist murders in the United States. In 2018, this statistic rose to 98% (The Anti-Defamation League Center on Extremism, 2019). The increasing severity of far-right extremist violence, as well as the associated rhetoric on social media (Davey and Ebner, 2019; Winter, 2019), has generated public concern about the spread of radicalization in the United States. Former extremists have referred to it as a public health issue (Allam, 2019; Bonn, 2019), an idea advocated for by some policy experts as well (Sanir et al., 2017; Weine and Eisenman, 2016).

There is little evidence that radicalization is primarily driven by psychopathology (Misiak et al., 2019; Post, 2015; Webber and Kruglanski, 2017). Rather, radicalization appears to be a process in which individuals are destabilized by various environmental factors, exposed to extremist ideology, and subsequently reinforced by members of their community (Becker, 2019; Jasko et al., 2017; Jensen et al., 2018; Mills et al., 2019; Webber and Kruglanski, 2017). Even “lone wolves”, or solo actors, often interact with extremist communities online (Holt et al., 2019; Kaplan et al., 2014; Post, 2015). As such, radicalization may spread through a social contagion process, in which extremist ideologies behave like complex contagions that require multiple exposures for adoption (Guilbeault et al., 2018), which has been observed for political movements more broadly (González-Bailón et al., 2011). Previous research suggests that extremist propaganda (Ferrara, 2017), hate crimes (Braun, 2011; Braun and Koopmans, 2010), intergroup conflict (Buhaug and Gleditsch, 2008; Gelfand et al., 2012), and terrorism (Cherif et al., 2009; LaFree et al., 2012; Midlarsky et al., 1980; White et al., 2016) exhibit similar dynamics.

Although social media platforms relax geographic constraints on communication, evidence suggests that social media networks still exhibit spatial clustering. For example, the majority of an individual’s Facebook friends live within 100 miles of them (Bailey et al., 2018), the probability of information diffusion on social media decays with increasing distance (Liu et al., 2018), and online echo chambers map onto particular locations (Bastos et al., 2018). Since complex contagions require reinforcement, and the majority of online friendship ties are within a close radius, the diffusion of extremist ideologies online should still exhibit some level of geographic bias. This idea is supported by evidence that social media enhances physical organizing among extremists (Bastug et al., 2018; Gill et al., 2017; von Behr et al., 2013), and anecdotes of “self-radicalized” individuals using social media to contact other extremists in their area (Holt et al., 2019).

In order to model the spread of far-right radicalization I used a two-component spatio-temporal intensity (twinstim) model (Meyer et al., 2017), an epidemiological method that treats events in space and time as resulting from self-exciting point processes (Reinhart, 2018). In this framework, future events depend on the history of past events within a certain geographic range. Event probabilities are determined by a conditional intensity function, which is separated into endemic and epidemic components. This allows researchers to assess the combined effects of both spatio-temporal covariates and epidemic predictors. Epidemic, in this framework, refers to any level of contagion effect and does not necessarily imply uncontrollable spread. With a couple of notable exceptions (Clark and Dixon, 2018; Zammit-Mangion et al., 2012), previous applications of self-exciting point process models in terrorism and mass shooting research have not simultaneously modeled diffusion over both time and space (Collins et al., 2020; Garcia-Bernardo et al., 2015; Johnson and Braithwaite, 2017; Lewis et al., 2012; Porter and White, 2010; Tench et al., 2016; Towers et al., 2015; White et al., 2013).

The radicalization events in this study, which correspond to where and when a radicalized individual’s extremist activity or plot was exposed, came from the Profiles of Individual Radicalization in the United States (PIRUS), an anonymized database compiled by the National Consortium for the Study of Terrorism and Responses to Terrorism (START) (National Consortium for the Study of Terrorism and Responses to Terrorism (START), University of Maryland, 2017). PIRUS is compiled from sources in the public record, and only includes individuals radicalized in the United States who were either arrested, indicted, or killed as a result of ideologically-motivated crimes, or were directly associated with a violent extremist organization. I chose to use PIRUS instead of the Terrorism and Extremist Violence in the United States (TEVUS) database because events in PIRUS are disambiguated by individual and include social variables that may influence the diffusion process.

A contagion effect in this modeling framework could result from one of two forces. The first is a copy-cat effect, in which individuals copy behaviors observed directly or in the media. Although this effect has been proposed in terrorism and mass shooting research in the past (Nacos, 2009; Towers et al., 2015), it seems to be a more plausible contagion mechanism for specific methods of violence (Helfgott, 2015) (e.g., suicide bombings (Tominaga, 2018)) rather than radicalization more broadly. The second is linkage triggered by activism and organizing, or ideologically-charged events (e.g., elections, demonstrations, policies), in that region. To differentiate between these two forces, I included two sets of epidemic predictors in the modeling. The first two event-level variables, plot success and anticipated fatalities, might be expected to increase epidemic probability if a copy-cat effect is present. This is because successful large-scale events are probably more contagious due to increased media coverage (Towers et al., 2015). Alternatively, the two individual-level variables, group membership and social media use, might be expected to increase epidemic probability if activism and organizing drive the linkage between events.

## Methods

### Data collection

All individual-level data came from PIRUS. Only individuals with far-right ideology who were exposed during or after 2005 (the earliest year with social media data) with location data at the city-level or lower (n = 416; F: 6.0%, M: 94.0%) were included (see Figs. 1 and 2). For each individual, the date and location of their exposure (usually when their activity/plot occurred), whether their plot was successful (34.9%), the anticipated fatalities of their plot (0: 69.5%, 1–20: 26.0%, >20:2.6%, >100: 1.9%), whether they were a member of a formal or informal group of extremists (58.4%), and whether social media played a role in their radicalization (31.2%), were included. Unknown or missing values for each predictor (plot success: 0.5%, anticipated fatalities: 13.5%, group membership: 0%, social media: 54.8%) were coded as 0. To ensure that the coding procedure for missing predictor values did not introduce bias, I checked whether the results of the full model were consistent after multiple imputation with chained equations and random forest machine learning (see Table S1). The location of each exposure was geocoded from the nearest city or town using the R package ggmap (Kahle and Wickham, 2013). Since domestic terrorists tend to commit acts in their local area (Klein et al., 2017; Marchment et al., 2018; Smith et al., 2008), I assumed that exposure locations reflect where individuals were radicalized.

State-level gun ownership was estimated using a proxy measure based on suicide rates and hunting licenses (Seigel et al., 2014). Using data from 2001, 2002, and 2004 (the only three years for which state-level gun ownership data is available), Seigel et al. found that the following proxy correlates with gun ownership with an R2 of 0.95:

$$\left(0.62\cdot \frac{{\mathrm{FS}}}{{\mathrm{S}}}\right)+(0.88\cdot {\mathrm{HL}})-0.0448$$
(1)

where FS/S is the proportion of suicides that involve firearms (from the Centers for Disease Control and Prevention, or CDC), and HL is hunting licenses per capita (from the United States Fish and Wildlife Service) (Seigel et al., 2014). Missing suicide rates (five years for DC, two years for Rhode Island) were replaced with the mean values for that state. State-level hate group data was collected from the Southern Poverty Law Center, while violent crime data was collected from the Federal Bureau of Investigation’s Uniform Crime Reporting Program.

County-level demographic data was collected from the US Census using the R package censusapi (Recht, 2019). This included population density, poverty rate, Gini index of income inequality, percentage of the population that is non-white, percentage of the population that has at least a high-school diploma, and unemployment rate. County-level income, race, education, and unemployment data is only available after 2009, so the 2010 data was used for 2005–2009. County-level presidential election voting records were collected from the Massachusetts Institute of Technology Election Lab, and non-election years were assigned the data from the most recent election year.

Geographic data was collected from the US Census using the R package tigris (Walker, 2019).

### Model specification

Twinstim modeling was conducted using the R package surveillance (Meyer et al., 2017). To convert the data to a continuous spatio-temporal point process, all tied locations and dates were shifted in a random direction up to half of the minimum spatial and temporal distance between events (1.52 km and 0.5 days, respectively) (Meyer and Held, 2014).

Step functions were used to model both spatial and temporal interactions. Visual inspection of the pair correlation function for the point pattern indicates that the data is significantly clustered up to 400 km (see Supplementary Fig. 1). As such, the spatial step function was split into four 100 km intervals with 400 km as the maximum interaction radius (Nightingale et al., 2015). The temporal step function was split into four six-month intervals up to two years (based on the the high degree of variation in radicalization and attack planning times among domestic extremists (Bouhana et al., 2018; Silkoset, 2016; Smith and Damphousse, 2009)). I attempted the analysis with different combinations of power-law, Gaussian, and Student spatial functions, and exponential temporal functions, but these variations converged to unrealistically steep spatial and temporal interaction functions that approached zero around two km and two days, and appeared to be significantly influenced by the tie-breaking procedure (Meyer and Held, 2014).

Population density (county-level) was log-transformed and used as an offset endemic term. A centered time trend was also included to determine whether the strength of the endemic component has shifted over time. Poverty rate (county-level), Gini index of income inequality (county-level), gun ownership (state-level), percentage of the population that is non-white (county-level), percentage of the population that has at least a high-school diploma (county-level), unemployment rate (county-level), percentage of voters that vote Republican in presidential elections (county-level), violent crime rate per thousand residents (state-level), and number of hate groups per million residents (state-level) were included as dynamic endemic predictors that change annually. Plot success, anticipated fatalities, group membership, and social media radicalization were included as epidemic predictors.

All possible models with all possible combinations of predictors were run and ranked by Akaike’s Information Criterion (AIC) (Burnham and Anderson, 2002). The best fitting model with the lowest AIC was used to assess the effects of each variable on event probability. Rate ratios were calculated by applying exponential transformation to the model estimates.

### Permutation test

To determine whether the spatio-temporal interaction of the epidemic component was statistically significant, I used the Monte Carlo permutation approach developed by Meyer et al. (Meyer et al., 2016). Using this approach, a twinstim model with all endemic predictors from the best fitting model and no epidemic predictors was compared to 1000 permuted null models with randomly shuffled event times. For each permutation I estimated the reproduction number (R0), or the expected number of future events that an event triggers on average, which represents “infectivity”. A p-value was calculated by comparing the observed R0 with the null distribution of the subset of permutations that converged.

For additional support, I also ran a likelihood ratio test and a standard Knox test of spatio-temporal clustering. The Knox test was conducted with spatial and temporal radii of 100 km and six months (the upper bounds of the first steps in the step functions), respectively (Knox and Bartlett, 1964).

### Simulations

To further assess the quality of the model, I conducted simulations from the cumulative intensity function using Ogata’s modified thinning algorithm according to Meyer et al. (2012). Using the parameters of the best fitting model, I conducted 1,000 simulations of the last six months of the study period and compared the results to the observed data.

## Results

The results of the best fitting model (ΔAIC < 2), which included seven endemic and two epidemic predictor variables, are shown in Table 1. Firstly, there is a statistically significant time trend whereby the endemic rate decreases by 4.6% each year, indicating that the strength of the epidemic component has increased over time. There appears to be a baseline increase in the endemic component between 2008-2012 which likely corresponds to the financial crisis (Funke et al., 2016), as well as a significant spike in the epidemic component around 2016 which likely corresponds to the presidential election (Giani and Meón, 2019; Rushin and Edwards, 2018) (Fig. 3). There are also significant positive effects of poverty rates (p < 0.01) and the presence of hate groups (p < 0.0001) on radicalization probability. Interestingly, the percentage of voters that vote Republican in presidential elections (p < 0.0001), the percentage of the population that is non-white (p < 0.05), and unemployment rates (p < 0.0001) appear to have significant negative effects on radicalization probability. Gun ownership, education level, and violent crime all have no significant effect on radicalization probability. When Republican voting was replaced with the absolute percent difference between Republican and Democratic voting, a proxy measure for the competitiveness of elections, it was no longer significant. A variance inflation factor test identified no multicollinearity problems among the time-averaged endemic predictors (VIF < 3) (Zuur et al., 2010).

Both group membership and radicalization via social media have strong and significant positive effects on epidemic probability. Exposures of individuals who belong to formal or informal extremist groups are over four times more likely to be followed by future exposures in close spatial or temporal proximity (p < 0.01). Similarly, exposures of individuals radicalized on social media are almost three times as likely to be followed by future exposures (p < 0.01). Anticipated fatalities and plot success did not appear in the best fitting model. Estimates of the decaying spatial and temporal interaction functions, as well as model diagnostics, can be seen in Supplementary Figs. 2 and 3, respectively. A variance inflation factor test identified no multicollinearity problems among the epidemic predictors (VIF < 3) (Zuur et al., 2010).

Based on the permutation test, the observed R0 (0.31) is significantly higher than the null distribution of the converged permutations (Nconv = 739, p < 0.01) (Fig. 4). This indicates that the spatio-temporal interaction in the epidemic model is significant. Both the likelihood ratio test of the epidemic against the endemic model (p < 0.0001) and the Knox test (p < 0.0001) support this result.

The results of the simulations can be seen in Figs. 5 and 6. On average the simulations neatly match the observed cumulative number of exposures between June 2017 and January 2018 (Fig. 5), indicating that the model accurately captures the temporal dynamics in the data. Similarly, the model appears to do a good job of capturing the spatial dynamics in the data, although it is clearly weighted towards high population density areas (Fig. 6).

## Discussion

By applying novel epidemiological methods to data on 416 extremists exposed between 2005 and 2017, this study provides evidence that patterns of far-right radicalization in the United States are consistent with a contagion process. Firstly, the estimated reproduction number is significantly higher than those from simulated null models, indicating that endemic causes alone are not sufficient to explain the spatio-temporal clustering observed in the data. The reproduction number for radicalization (R0 = 0.31) is also lower than one, suggesting that extremist ideologies behave like complex contagions that require reinforcement for transmission. Fortunately, this means that extremist ideologies are unlikely to spread uncontrollably through populations like seasonal influenza (R0 = 1.28) (Biggerstaff et al., 2014), but outbreaks can occur under the right endemic and epidemic conditions. For example, regions with higher rates of poverty and hate group activity are more likely to experience far-right extremism, whereas regions with a larger non-white population, more Republican voting, and higher rates of unemployment are less likely to experience far-right extremism. Most importantly, radicalizations involving extremist groups or social media significantly increase the epidemic probability of future radicalizations in the same location. This suggests that clusters of radicalizations in space and time are driven by activism and organizing rather than a copy-cat effect.

The fact that group membership significantly increases the epidemic strength of events, and the presence of hate groups significantly increases radicalization probability, suggests that local organizing remains a potent recruitment tool of the far-right movement. This idea is reflected in recent increases in rallies across the country, such as “Unite the Right” in Charlottesville, VA in August of 2017, that have been attended by regional chapters of white nationalist and militia organizations. It also suggests that concerns about typological “lone wolves” radicalized over social media should not overshadow the persistent and expanding far-right movement in the United States. Only 10.8% of people in this study were radicalized on social media independently of an extremist group, indicating that solo actors are still the minority in the far-right movement. That being said, solo actors radicalized on social media, such as Omar Mateen (Pulse nightclub shooting in 2016) and Dylann Roof (Charleston church shooting in 2015) (Holt et al., 2019), are typically deadlier than group members in the United States (Phillips, 2017), and should thus be the subject of much future research.

Radicalization on social media also significantly increases the epidemic strength of events, indicating that social media platforms augment physical organizing and that the diffusion of extremist ideologies online is likely geographically biased. The increasing role of social media in far-right extremism and radicalization is well established (Costello and Hawdon, 2018; Holt et al., 2019; Lowe, 2019; Ottoni et al., 2018; Winter, 2019). Social media platforms like Twitter provide extremist communities with low cost access to large audiences that might not otherwise engage with far-right content (Bertram, 2016; Wu, 2015). For example, one report found that only 44% of people who follow high-profile white nationalists on Twitter overtly express similar ideologies (Berger and Strathearn, 2013). As mainstream platforms clamp down on hate speech, extremist users have just shifted their traffic to alternative sites such as 8chan and Gab (Blackbourn et al., 2019; Hodge and Hallgrimsdottir, 2019). Given the centrality of social media in far-right organizing, future research should explore how counter-narratives (van Eerten et al., 2017; Voogt, 2017) and other strategies could be used to fight the spread of extremist ideologies online.

The results indicate that county-level poverty rates increase the probability of far-right radicalization. While there is little to no evidence that poverty predicts extremism at the state-level (Durso and Jacobs, 2013; Gale et al., 2002; Lin et al., 2018; Piazza, 2017), studies at the county-level have found that poverty predicts both mass shooting rate (Kwon and Cabrera, 2019b) and hate groups (presence (Medina et al., 2018) not longevity (Suttmoeller et al., 2015, 2016, 2018)). This discrepancy between geographic resolutions indicates that using state-level poverty data obscures local variation. The results of this study also reveal a negative effect of unemployment rate on radicalization, adding to the remarkably contradictory evidence for links between unemployment and extremism in the United States (Espiritu, 2004; Gale et al., 2002; Goetz et al., 2012; Green et al., 1998, Jefferson and Pryor, 1999; Majumder, 2017; Piazza, 2017). Although this result appears to be counter-intuitive, I hypothesize that poverty and unemployment may interact in driving radicalization. For example, individuals from regions where jobs are plentiful but poverty remains high may be the most disillusioned and susceptible to extremist ideologies. Interestingly, income inequality did not appear in the best fitting model, and had no significant effect when included. This suggests that overall deprivation, as measured by poverty rate, is more important in driving radicalization than inequality. Previous studies that have found a positive impact of income inequality on hate groups or crime either used state-level data (Majumder, 2017), did not account for poverty rate (Goetz et al., 2012; McVeigh, 2004), or combined income inequality with poverty rate into a single index (McVeigh and Cunningham, 2012). Interestingly, both unemployment (Pah et al., 2017) and income inequality (Kwon and Cabrera, 2017, 2019a, b) appear to be strong predictors of mass shootings. Although this seems paradoxical, the majority of mass shootings are not ideologically driven (Capellan, 2015), so the socioeconomic drivers may be different than for far-right radicalization.

Violent crime appears to have no influence on radicalization. Although one study of the Ku Klux Klan found that high levels of far-right activity can increase homicide rates in the long-term (McVeigh and Cunningham, 2012), there is little evidence that violent crime rates drive increases in extremist violence or radicalization (Sweeney and Perliger, 2018). Hate crime is only very weakly correlated with violent crime (Gladfelter et al., 2017), and extremist violence is even more rare (LaFree and Dugan, 2009), so they are likely driven by different factors.

Previous studies have found strong evidence for a negative relationship between education and hate crime rates (Espiritu, 2004; Gladfelter et al., 2017), a positive relationship between education and mass shooting rates (Kwon and Cabrera, 2017, 2019a), and no evidence for a relationship between education and hate group organizing (Durso and Jacobs, 2013; Florida, 2011; McVeigh et al., 2014). The results of this study are consistent with the latter category, which makes sense given that the majority of the plots in the dataset were non-violent.

The negative effect of Republican voting on event probability could be because individuals on the far-right of the political spectrum who live in counties with more Democratic voters may feel more partisan hostility (Miller and Conover, 2015). Interestingly, this effect does not appear to be the result of more competitive elections (Suttmoeller et al., 2015), as the absolute difference between Republican and Democratic voting did not significantly influence event probability. Alternatively, the negative effect of Republican voting may be due to the fact that many of the rural counties that lean heavily Republican have low population densities and no recent history of extremist violence. A previous study that found mixed evidence for a positive influence of Republican voting on the presence of hate groups excluded counties without hate groups from the modeling, which may have eliminated this skew effect (Medina et al., 2018).

The fact that the percentage of the population that is non-white negatively predicts far-right extremist violence is consistent with the intergroup contact hypothesis, which suggests that prolonged contact between racial groups reduces conflict under certain conditions (Allport, 1954). Although other researchers have suggested that population heterogeneity increases far-right radicalization (McVeigh, 2004), the only study to find evidence of this in the United States did not explicitly account for population density (LaFree and Bersani, 2014). Other studies controlling for population density have found that both anti-black hate crimes and hate groups appear to be more common in white dominated, racially homogeneous areas (Gladfelter et al., 2017; Medina et al., 2018). Despite mixed evidence for the intergroup contact hypothesis, it is widely accepted that community diversity and tolerance is key to fighting radicalization and extremist violence globally (Ellis and Abdi, 2017; Ercan, 2017; Gunaratna et al., 2013; Hoffman et al., 2018; Southern Poverty Law Center, 2017; United Nations Development Programme, 2016).

Gun ownership does not predict radicalization in this model, which is unsurprising since only 30.5% of people in this study planned on committing fatal attacks but interesting given the centrality of gun control in debates following mass shootings in the United States (Joslyn and Haider-Markel, 2017; Luca et al., 2020; Pierre, 2019). Despite strong evidence that gun ownership is linked to mass shooting rates at the national-level (Reeping et al., 2019), evidence for same pattern at the state-level remains mixed. Previous studies have found that it either positively predicts mass shootings overall (Reeping et al., 2019), when combined with particular gun control laws (Anisin, 2018), or not at all (Lin et al., 2018; Pah et al., 2017). Unfortunately, CDC funding for research on gun ownership was restricted by Congress in 1996 after lobbying by the National Rifle Association, so potential links between extremist violence and gun ownership remain understudied (DeFoster and Swalve, 2018; Lemieux, 2014; Morall, 2018; Winker et al., 2016).

Several limitations of this study should be highlighted. Firstly, the PIRUS database only represents a subset of radicalized individuals in the United States. The creators of the database used random sampling to maximize its representativeness over different time periods, but there remains a possibility of spatial or temporal bias in the original data due to underreporting by victims and law enforcement effort (DiIulio, 1996). Instances of hate crime are notoriously underreported relative to other forms of crime (Pezzella et al., 2019), because victims often fear retaliation or mistrust the police (Pezzella, 2017; Weiss et al., 2016; Wong and Christmann, 2016). There is also a great deal of variation in hate crime training among police departments, and the personal beliefs of individual officers can influence whether or not instances are reported (Boyd et al., 1996; Pezzella, 2017). Both of these factors are likely to be more pronounced in areas with legacies of far-right extremist violence, and historical crossover between far-right groups and the police (Barnes, 1996; Johnson, 2019; Rowe, 1976). In addition, the geographic locations of events are only geocoded to the city-level, potentially enhancing the spatial clustering of the data. Furthermore, social media data were missing for a significant number of individuals (54.8%). The significance level of the estimate for social media usage is extremely low and robust to imputation, indicating that it likely reflects a real effect, but researchers should exercise caution when interpreting this result (Safer-Lichtenstein et al., 2017). Lastly, the spatial resolution of three of the endemic predictors was limited to the state-level, which may have flattened some important local variation. One of these variables, gun ownership, was also a proxy measure. Policymakers should release historical restrictions on research funding for gun violence and hate crime research to improve data resolution for future studies.

In conclusion, far-right radicalization in the United States appears to spread through populations like a complex contagion. Both social media usage and group membership enhance the contagion process, indicating that online and physical organizing remain primary recruitment tools of the far-right movement. In addition, far-right radicalization is more likely in Democrat-majority regions with high poverty and low unemployment, fewer non-white people, and more hate group activity. While the federal government has acknowledged the threat of far-right extremism (The Department of Homeland Security, 2019), funding for organizations researching or fighting the movement has decreased in recent years (O’Toole, 2019). Based on the results of this study, I recommend that policymakers reconsider their funding priorities to address the expanding far-right extremist movement in the United States. Future research should investigate how specific interventions, such as online counter-narratives to battle propaganda, may be effectively implemented to mitigate the spread of extremist ideology.

## Data availability

All data used in the study are available online either publicly or upon request from PIRUS. The R code used in the study is available on Harvard Dataverse: https://doi.org/10.7910/DVN/WPYCKJ

## References

1. Adamczyk A, Gruenewald J, Chermak SM, Freilich JD (2014) The relationship between hate groups and far-right ideological violence. J Contemp Crim Justice 30(3):310–332

2. Allam H (2019) ‘We were blindsided’: families of extremists form group to fight hate. National Public Radio (12)

3. Allport G (1954) The nature of prejudice. Addison-Wesley, Cambridge

4. Aly A, Macdonald S, Jarvis L, TM Chen (2017) Introduction to the special issue: terrorist online propaganda and radicalization. Stud Confl Terror 40(1):1–9

5. Amble JC (2012) Combating terrorism in the new media environment. Stud Confl Terror 35(5):339–353

6. Anisin A (2018) A configurational analysis of 44 US mass shootings: 1975-2015. Int J Comparat Appl Criminal Justice 42(1):55–73

7. Awan I (2017) Cyber-extremism: Isis and the power of social media. Society 54(2):138–149

8. Bailey M, Cao R, Kuchler T, Stroebel J, Wong A (2018) Social connectedness: measurement, determinants, and effects. J Econ Perspect 32(3):259–280

9. Barnes RD (1996) Blue by day and white by (k)night: regulating the political affiliations of law enforcement and military personnel. Iowa Law Rev 81:1079

10. Bastos M, Mercea D, Baronchelli A (2018) The geographic embedding of online echo chambers: evidence from the Brexit campaign. PLoS ONE 13(11):1–16

11. Bastug M, Douai A, Akca D (2018) Exploring the "demand side” of online radicalization: evidence from the Canadian context. Stud Confl Terror. https://doi.org/10.1080/1057610X.2018.1494409

12. Becker MH (2019) When extremists become violent: examining the association between social control, social learning, and engagement in violent extremism. Stud Confl Terror. https://doi.org/10.1080/1057610X.2019.1626093

13. Berger JM, Strathearn B (2013) Who matters online: measuring influence, evaluating content and countering violent extremism in online social networks. The International Centre for the Study of Radicalisation and Political Violence. https://bit.ly/35lvqby

14. Bertram L (2016) Terrorism, the Internet, and the Social Media Advantage: Exploring how terrorist organizations exploit aspects of the internet, social media and how these same platforms could be used to counter-violent extremism. J Deradical 7:225–252

15. Biggerstaff M, Cauchemez S, Reed C, Gambhir M, Finelli L (2014) Estimates of the reproduction number for seasonal, pandemic, and zoonotic influenza: a systematic review of the literature BMC Infect Dis 14:480

16. Blackbourn J, McGarrity N, Roach K (2019) Understanding and responding to right wing terrorism. J Polic Intell Count Terror 14(3):183–190

17. Bonn T (2019) Former extremists call for violent extremism to be treated as public health issue. The Hill (9)

18. Bouhana N, Corner E, Gill P, Schuurman B (2018) Background and preparatory behaviours of right-wing extremist lone actors: a comparative study. Perspect Terror 12(6):150–163

19. Bowman-Grieve L (2009) Exploring stormfront: a virtual community of the radical right. Stud Confl Terror 32(11):989–1007

20. Boyd EA, Berk RA, Hamner KM (1996) "Motivated by hatred or prejudice”: categorization of hate-motivated crimes in two police divisions. Law Soc Rev 30(4):819–850

21. Braun R (2011) The diffusion of racist violence in the Netherlands: discourse and distance. J Peace Res 48(6):753–766

22. Braun R, Koopmans R (2010) The diffusion of ethnic violence in Germany: the role of social similarity. Eur Sociol Rev 26(1):111–123

23. Buhaug H, Gleditsch KS (2008) Contagion or confusion? why conflicts cluster in space. Int Stud Q 52(2):215–233

24. Burnham KP, Anderson DR (2002) Model selection and multimodel inference: a practical information-theoretic approach. Springer, New York

25. Capellan JA (2015) Lone wolf terrorist or deranged shooter? a study of ideological active shooter events in the United States, 1970-2014. Stud Confl Terror 38(6):395–413

26. Cherif A, Yoshioka H, Ni W, Bose P (2009) Terrorism: mechanisms of radicalization processes, control of contagion and counter-terrorist measures. Preprint at arXiv: 0910.5272

27. Clark NJ, Dixon PM (2018) Modeling and estimation for self-exciting spatio-temporal models of terrorist activity. Ann Appl Stat 12(1):633–653

28. Collins B, Hoang DT, Yoon HJ, Nguyen NT, Hwang D (2020) A survey on forecasting models for preventing terrorism. In: Advanced computational methods for knowledge engineering. Springer, Cham, pp 323–334

29. Costello M, J Hawdon (2018) Who are the online extremists among us? sociodemographic characteristics, social networking, and online experiences of those who produce online hate materials. Violence Gender 5(1):55–60

30. Davey J, Ebner J (2019) ‘The great replacement’: the violent consequences of mainstreamed extremism. Institute for Strategic Dialogue. https://bit.ly/2yXdl7h

31. Dean G, Bell P, Newman J (2012) The dark side of social media: review of online terrorism. Pak J Criminol 3(3):107–126

32. DeFoster R, Swalve N (2018) Guns, culture or mental health? framing mass shootings as a public health crisis. Health Commun 33(10):1211–1222

33. DiIulio JJ (1996) Help wanted: economists, crime and public policy. J Econ Perspect 10(1):3–24

34. Durso RM, Jacobs D (2013) The determinants of the number of white supremacist groups: a pooled time-series analysis. Soc Probl 60(1):128–144

35. Ellis BH, Abdi S (2017) Building community resilience to violent extremism through genuine partnerships. Am Psychol 72(3):289–300

36. Ercan SA (2017) Engaging with extremism in a multicultural society: a deliberative democratic approach. J Peacebuild Dev 12(2):9–21

37. Espiritu A (2004) Racial diversity and hate crime incidents. Soc Sci J 41(2):197–208

38. Ferrara E (2017) Contagion dynamics of extremist propaganda in social networks. Inf Sci 418-419:1–12

39. Florida R (2011) The geography of hate. The Atlantic (5)

40. Funke M, Schularick M, Trebesch C (2016) Going to extremes: politics after financial crises, 1870-2014. Eur Econ Rev 88(2011):227–260

41. Gale LR, Heath WC, Ressler RW (2002) An economic analysis of hate crime. East Econ J 28(2):203–216

42. Garcia-Bernardo J, Qi H, Shultz JM, Cohen AM, Johnson NF, Dodds PS (2015) Social media affects the timing, location, and severity of school shootings. Preprint at arXiv: 1506.06305

43. Gelfand M, Shteynberg G, Lee T, Lun J, Lyons S, Bell C, Chiao JY, Bruss CB, Dabbagh MA, Aycan Z, Abdel-Latif AH, Dagher M, Khashan H, Soomro N (2012) The cultural contagion of conflict. Philos Trans R Soc B 367(1589):692–703

44. Giani M, Meón PG (2019) Global racist contagion following Donald Trump’s election. Br J Polit Sci. https://doi.org/10.1017/S0007123419000449

45. Gill P, Corner E, Conway M, Thornton A, Bloom M, Horgan J (2017) Terrorist use of the internet by the numbers: quantifying behaviors, patterns, and processes. Criminol Public Policy 16(1):99–117

46. Gladfelter AS, Lantz B, Ruback RB (2017) The complexity of hate crime and bias activity: variation across contexts and types of bias. Justice Q 34(1):55–83

47. Goetz SJ, Rupasingha A, Loveridge S (2012) Social capital, religion, Wal-Mart, and hate groups in America. Soc Sci Q 93(2):379–393

48. González-Bailón S, Borge-Holthoefer J, Rivero A, Moreno Y (2011) The dynamics of protest recruitment through an online network. Sci Rep 1(197):1–7

49. Green DP, Glaser J, Rich A (1998) From lynching to gay bashing: the elusive connection between economic conditions and hate crime. J Pers Soc Psychol 75(1):82–92

50. Guilbeault D, Becker J, Centola D (2018) Complex contagions: a decade in review. In: Complex spreading phenomena in social systems. Springer, Cham, pp 3–25

51. Gunaratna R, Jerard J, Nasir SM (2013) Countering extremism: building social resilience through community engagement. Imperial College Press, London

52. Helfgott JG (2015) Criminal behavior and the copycat effect: literature review and theoretical framework for empirical investigation. Aggress Violent Behav 22:46–64

53. Hodge E, Hallgrimsdottir H (2019) Networks of hate: the alt-right, “troll culture”, and the cultural geography of social movement spaces online. J Borderl Stud https://doi.org/10.1080/08865655.2019.1571935

54. Hoffman AJ, Alamilla S, Liang B (2018) The role of community development in reducing extremism and ethnic conflict. Palgrave MacMillan, Cham

55. Holt TJ, Freilich JD, Chermak SM (2016) Internet-based radicalization as enculturation to violent deviant subcultures. Deviant Behav 38(8):855–869

56. Holt TJ, Freilich JD, Chermak SM, Mills C, Silva J (2019) Loners, colleagues, or peers? assessing the social organization of radicalization. Am J Crim Justice 44(1):83–105

57. Jasko K, LaFree G, Kruglanski A (2017) Quest for significance and violent extremism: the case of domestic radicalization. Polit Psychol 38(5):815–831

58. Jefferson PN, Pryor FL (1999) On the geography of hate. Econ Lett 65(3):389–395

59. Jensen MA, Seate AA, James PA (2018) Radicalization to violence: a pathway approach to studying extremism. Terror Polit Violence. https://doi.org/10.1080/09546553.2018.1442330

60. Johnson VB (2019) KKK in the PD: white supremacist police and what to do about it. Lewis Clark Law Rev 23(1):205–261

61. Johnson SD, Braithwaite A (2017) Spatial and temporal analysis of terrorism and insurgency. In: The handbook of the criminology of terrorism. Wiley, Hoboken, pp 232–243

62. Joslyn MR, Haider-Markel DP (2017) Gun ownership and self-serving attributions for mass shooting tragedies. Soc Sci Q 98(2):429–442

63. Kahle D, Wickham H (2013) ggmap: spatial visualization with ggplot2. R J 5(1):144–161

64. Kaplan J, Lööw H, L Malkki (2014) Introduction to the special issue on lone wolf and autonomous cell terrorism. Terror Polit Violence 26(1):1–12

65. Klein BR, Gruenewald J, Smith BL (2017) Opportunity, group structure, temporal patterns, and successful outcomes of far-right terrorism incidents in the United States. Crime Delinq 63(10):1224–1249

66. Knox EG, Bartlett MS (1964) The detection of space-time interactions. J Royal Stat Soc C 13(1):25–30

67. Kwon R, Cabrera JF (2017) Socioeconomic factors and mass shootings in the United States. Crit Public Health 28(2):138–145

68. Kwon R, Cabrera JF (2019a) Income inequality and mass shootings in the United States. BMC Public Health 19:1147

69. Kwon R, Cabrera JF (2019b) Social integration and mass shootings in U.S. counties. J Crime Justice 42(2):121–139

70. LaFree G, Bersani BE (2014) County-level correlates of terrorist attacks in the United States. Criminol Public Policy 13(3):455–481

71. LaFree G, Dugan L (2009) Tracking global terrorism trends, 1970-2004. In: To protect and to serve: policing in an age of terrorism. Springer, New York, pp 43–80

72. LaFree G, Dugan L, Xie M, P Singh (2012) Spatial and temporal patterns of terrorist attacks by ETA 1970 to 2007. J Quant Criminol 28(1):7–29

73. Lemieux F (2014) Effect of gun culture and firearm laws on gun violence and mass shootings in the United States: a multi-level quantitative analysis. Int J Crim Justice Sci 9(1):74–93

74. Lewis E, Mohler G, Brantingham PJ, Bertozzi AL (2012) Self-exciting point process models of civilian deaths in Iraq. Security J 25(3):244–264

75. Lin PI, Fei L, Barzman D, Hossain M (2018) What have we learned from the time trend of mass shootings in the U.S.? PLoS ONE 13(10):1–13

76. Liu L, Chen B, Ai C, He L, Wang Y, Qiu X, Lu X (2018) The influence of geographic factors on information dissemination in mobile social networks in China: evidence from WeChat. ISPRS Int J Geoinf 7(5):1–16

77. Lowe D (2019) The Christchurch terrorist attack, the far-right, and social media: what can we Learn? The New Jurist (4)

78. Luca M, Malhotra D, Poliquin C (2020) The impact of mass shootings on gun policy. J Public Econ 181:104083

79. Majumder M (2017) Higher rates of hate crimes are tied to income inequality. FiveThirtyEight (1)

80. Marchment Z, Bouhana N, Gill P (2018) Lone actor terrorists: a residence-to-crime approach. Terror Political Violence. https://doi.org/10.1080/09546553.2018.1481050

81. McVeigh R (2004) Structured ignorance and organized racism in the United States. Soc Forces 82(3):895–936

82. McVeigh R, Cunningham D (2012) Enduring consequences of right-wing extremism: Klan mobilization and homicides in southern counties. Soc Forces 90(3):843–862

83. McVeigh R, Cunningham D, Farrell J (2014) Political polarization as a social movement outcome: 1960s Klan activism and its enduring impact on political realignment in southern counties, 1960 to 2000. Am Sociol Rev 79(6):1144–1171

84. Medina RM, Nicolosi E, Brewer S, Linke AM (2018) Geographies of organized hate in America: a regional analysis. Ann Am Assoc Geogr 108(4):1006–1021

85. Meyer S, Elias J, Höhle M (2012) A space-time conditional intensity model for invasive meningococcal disease occurrence. Biometrics 68(2):607–616

86. Meyer S, Held L (2014) Power-law models for infectious disease spread. Ann Appl Stat 8(3):1612–1639

87. Meyer S, Held L, Höhle M (2017) Spatio-temporal analysis of epidemic phenomena using the R package surveillance. J Stat Softw 77(11):1–55

88. Meyer S, Warnke I, Rössler W, Held L (2016) Model-based testing for space-time interaction using point processes: an application to psychiatric hospital admissions in an urban area. Spat Spatio-Temporal Epidemiol 17:15–25

89. Midlarsky MI, Crenshaw M, Yoshida F (1980) Why violence spreads: the contagion of international terrorism. Int Stud Q 24(2):262–298

90. Miller PR, Conover PJ (2015) Red and blue states of mind: partisan hostility and voting in the United States. Polit Res Q 68(2):225–239

91. Mills CE, Freilich JD, Chermak SM, Holt TJ, LaFree G (2019) Social learning and social control in the off- and online pathways to hate crime and terrorist violence. Stud Confl Terror. https://doi.org/10.1080/1057610X.2019.1585628

92. Misiak B, Samochowiec J, Bhui K, Schouler-Ocak M, Demunter H, Kuey L, Raballo A, Gorwood P, Frydecka D, Dom G (2019) A systematic review on the relationship between mental health, radicalization and mass violence. Eur Psychiatry 56:51–59

93. Morall A (2018) The science of gun policy: a critical synthesis of research evidence on the effects of gun policies in the united states. RAND Health Quart 8:1

94. Nacos BL (2009) Revisiting the contagion hypothesis: terrorism, news coverage, and copycat attacks. Perspect Terror 3(3):3–13

95. National Consortium for the Study of Terrorism and Responses to Terrorism (START), University of Maryland (2017). Profiles of Individual Radicalization in the United States (PIRUS). https://bit.ly/2yWtmu8

96. Nightingale GF, Laland KN, Hoppitt W, Nightingale P (2015) Bayesian spatial NBDA for diffusion data with home-base coordinates. PLoS ONE 10(7):e0130326

97. O’Toole M (2019) Trump officials have redirected resources from countering far-right, racism-fueled domestic terrorism. Los Angeles Times (8)

98. Ottoni R, Bernardina P, Cunha E, Meira W, Magno G, Almeida V (2018) Analyzing right-wing YouTube channels: hate, violence and discrimination. In: WebSci 2018 Proceedings of the 10th ACM Conference On Web Science, Amsterdam, pp 323–332

99. Pah AR, Hagan J, Jennings AL, Jain A, Albrecht K, Hockenberry AJ, Amaral LA (2017) Economic insecurity and the rise in gun violence at US schools. Nat Hum Behav 1(2):2–7

100. Pauwels L, Brion F, Schils N, Laffineur J, Verhage A, de Ruyver B, Easton M (2014) Explaining and understanding the role of exposure to new social media in violent extremism: an integrative quantitative and qualitative approach. Academia Press, Gent

101. Pezzella FS (2017) Hate crime statutes: a public policy and law enforcement dilemma. Springer, New York

102. Pezzella FS, Fetzer MD, Keller T (2019) The dark figure of hate crime underreporting. Am Behav Sci. https://doi.org/10.1177/0002764218823844

103. Phillips BJ (2017) Deadlier in the U.S.? on lone wolves, terrorist groups, and attack lethality. Terror Polit Violence 29(3):533–549

104. Piazza JA (2017) The determinants of domestic right-wing terrorism in the USA: economic grievance, societal change and political resentment. Confl Manag Peace Sci 34(1):52–80

105. Pierre JM (2019) The psychology of guns: risk, fear, and motivated reasoning. Pal Commun 5(1):1–7

106. Porter MD, White G (2010) Self-exciting hurdle models for terrorist activity. Ann Appl Stat 4(1):106–124

107. Post JM (2015) Terrorism and right-wing extremism: the changing face of terrorism and political violence in the 21st century: the virtual community of hatred. Int J Group Psychoth 65(2):242–271

108. Recht H (2019) censusapi: retrieve data from the census APIs. R package version 0.6.0

109. Reeping PM, Cerdá M, Kalesan B, Wiebe DJ, Galea S, Branas CC (2019) State gun laws, gun ownership, and mass shootings in the US: cross sectional time series. BMJ 364:1542

110. Reinhart A (2018) A review of self-exciting spatio-temporal point processes and their applications. Stat Sci 33(3):299–318

111. Rowe G (1976) My undercover years with the Ku Klux Klan. Bantam Books, New York

112. Rushin S, Edwards GS (2018) The effect of President Trump’s election on hate crimes. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.3102652

113. Safer-Lichtenstein A, LaFree G, Loughran T (2017) Studying terrorism empirically: what we know about what we donat know. J Contemp Crim Justice 33(3):273–291

114. Sanir J, Nicholson A, Giammaria C (2017) Countering violent extremism through public health practice: proceedings of a workshop. In: Forum on medical and public health preparedness for disasters and emergencies. The National Academies Press, Washington, DC

115. Seigel M, Ross C, King C (2014) A new proxy measure for state-level gun ownership in studies of firearm injury prevention. Inj Prev 20(3):204–207

116. Silkoset E (2016) Lone-actor terrorists: how long does it take to plan a terrorist attack? Dissertation, University College of London

117. Simi P, Bubolz BF (2017) Far right terrorism in the United States. In: The handbook of the criminology of terrorism, Wiley, Hoboken. pp 297–309

118. Smith BL, Cothren J, Roberts P, Damphousse KR (2008) Geospatial analysis of terrorist activities: the identification of spatial and temporal patterns of preparatory behavior of international and environmental terrorists. Terrorism Research Center in Fulbright College, University of Arkansas. https://bit.ly/2SibIIc

119. Smith BL, Damphousse KR (2009) Patterns of precursor behaviors in the life span of a U.S. environmental terrorist group. Criminol Public Policy 8(3):475–496

120. Southern Poverty Law Center (2017) Ten ways to fight hate: a community resource guide. https://bit.ly/35j4TLN

121. Suttmoeller M, Chermak S, Freilich JD (2015) The influence of external and internal correlates on the organizational death of domestic far-right extremist groups. Stud Confl Terror 38(9):734–758

122. Suttmoeller MJ, Chermak SM, Freilich JD (2016) Only the bad die young: the correlates of organizational death for far-right extremist groups. Stud Confl Terror 39(6):477–499

123. Suttmoeller MJ, Chermak SM, Freilich JD (2018) Is more violent better? the impact of group participation in violence on group longevity for far-right extremist groups. Stud Confl Terror 41(5):365–387

124. Sweeney MM, Perliger A (2018) Explaining the spontaneous nature of far-right violence in the United States. Perspect Terror 12(6):52–71

125. Tench S, Fry H, Gill P (2016) Spatio-temporal patterns of IED usage by the Provisional Irish Republican Army. Eur J Appl Math 27(3):377–402

126. The Anti-Defamation League Center on Extremism (2019) Murder and extremism in the United States in 2018. https://bit.ly/2VLy5If

127. The Department of Homeland Security (2019) Strategic framework for countering terrorism and target violence. https://bit.ly/2xhCCsB

128. Tominaga Y (2018) Thereas no place like home! examining the diffusion of suicide attacks through terrorist group locations. Appl Spat Anal Policy 11(2):355–379

129. Towers S, Gomez-Lievano A, Khan M, Mubayi A, Castillo-Chavez C (2015) Contagion in mass killings and school shootings. PLoS ONE 10(7):e0117259

130. United Nations Development Programme (2016) Preventing violent extremism through promoting inclusive development, tolerance and respect for diversity. https://bit.ly/2KJzxVa

131. van Eerten JJ, Doosje B, Konijn E, de Graaf B, de Goede M (2017) Developing a social media response to radicalization: the role of counter-narratives in prevention of radicalization and de-radicalization. Wetenschappelijk Onderzoek-en Documentatiecentrum. https://bit.ly/2VMRkBc

132. von Behr I, Reding A, Edwards C, Gribbon L (2013) Radicalisation in the digital era: the use of the internet in 15 cases of terrorism and extremism. RAND Europe. https://bit.ly/37AOnIn

133. Voogt S (2017) Countering far-right recruitment online: CAPEas practitioner experience. J Polic Intelligence Counter Terrorism 12(1):34–46

134. Walker K (2019) tigris: load vensus TIGER/line shapefiles. R package version 0.8.2

135. Webber D, Kruglanski AW (2017) Psychological factors in radicalization: a “3 N” approach. In: The handbook of the criminology of terrorism. Wiley, Hoboken, pp 33–46

136. Weine S, Eisenman, D (2016) How public health can improve initiatives to counter violent extremism. National Consortium for the Study of Terrorism and Responses to Terrorism. https://bit.ly/3cVtvNm

137. Weiss JC, McDevitt J, Iwama JA (2016) Group work with victims of hate crimes. In: Greif GL, Knight C (ed) Group work with populations at risk, 4th edn. Oxford, New York, pp 291–311

138. White G, Porter MD, Mazerolle L (2013) Terrorism risk, resilience and volatility: a comparison of terrorism patterns in three southeast Asian countries. J Quant Criminol 29(2):295–320

139. White G, Ruggeri F, Porter MD (2016) Modelling the proliferation of terrorism via diffusion and contagion. Preprint at arXiv 1612.02527

140. Winker MA, Abbasi K, Rivara FP (2016) Unsafe and understudied: the US gun problem. BMJ 352:i578

141. Winter A (2019) Online hate: from the far-right to the ‘alt-right’ and from the margins to the mainstream. In: Online Othering. Springer, Cham, pp 39–63

142. Wong K, Christmann K (2016) Increasing hate crime reporting: narrowing the gap between policy aspiration, victim inclination and agency capability. Br J Commun Justice 14(3):5–23

143. Wu P (2015) Impossible to regulate? social media, terrorists, and the role for the U.N. Chic J Int Law 16(1):281–311

144. Zammit-Mangion A, Dewar M, Kadirkamanathan V, Sanguinetti G (2012) Point process modelling of the Afghan War Diary. PNAS 109(31):12414–12419

145. Zuur AF, Ieno EN, Elphick CS (2010) A protocol for data exploration to avoid common statistical problems. Methods Ecol Evol 1(1):3–14

## Acknowledgements

I would like to thank David Lahti, Bobby Habig, and the rest of the Lahti lab for their valuable conceptual feedback.

## Author information

Authors

### Corresponding author

Correspondence to Mason Youngblood.

## Ethics declarations

### Competing interests

The author declares no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Rights and permissions

Reprints and Permissions