Forecasting the locational dynamics of transnational terrorism: a network analytic approach
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Abstract
Abstract
Efforts to combat and prevent transnational terrorism rely, to a great extent, on the effective allocation of security resources. Critical to the success of this allocation process is the identification of the likely geopolitical sources and targets of terrorism. We construct the network of transnational terrorist attacks, in which source (sender) and target (receiver) countries share a directed edge, and we evaluate a network analytic approach to forecasting the geopolitical sources and targets of terrorism. We integrate a deterministic, similarity-based, link prediction framework into a probabilistic modeling approach in order to develop an edge-forecasting method. Using a database of over 12,000 transnational terrorist attacks occurring between 1968 and 2002, we show that probabilistic link prediction is not only capable of accurate forecasting during a terrorist campaign, but is a promising approach to forecasting the onset of terrorist hostilities between a source and a target.
Keywords
Terrorist Attack Link Prediction Proximity Measure Terrorist Threat Exponential Random Graph ModelIntroduction
The accurate forecasting of transnational terrorism is among the most pressing problems of contemporary security policy. Counter-terrorism efforts may be greatly aided if resources, ranging from analytic focus to prevention capabilities, can effectively target the source of terrorist threats before terrorists can launch attacks. Traditional efforts to statistically forecast terrorism are complicated by the fact that most forecasting models perform best when there is a long series of data to study, thus rendering them impotent for identifying new sources of threat and forecasting attacks from sources that have not attacked before. For example, a protracted terrorist campaign may provide enough data for accurate time-series forecasting, but, from a policy perspective, may not be useful because the target government already understands that it is under attack from that source. The major challenge in forecasting transnational terrorism, as we see it, is identifying sources of threat (countries who’s nationals conduct terrorist attacks against a given target state) before any attacks from that source have been observed and quantifying the extent of the threat.
We approach the problem of forecasting transnational terrorism from a network analytic perspective with the supposition that the structure of the transnational terrorist network may be the best predictor of its own evolution. We construct the global transnational terrorism network, in which a directed edge exists from the state that produces a transnational terrorist to the state attacked by that terrorist, using the ITERATE dataset[1]. The data cover more than 12,000 transnational terrorist attacks between 1968 and 2002. We create an edge forecasting framework for the transnational terrorist network by integrating a deterministic similarity-based edge prediction method developed by Liben-Nowell and Kleinberg[2] with a model-based probabilistic approach developed by Hanneke, Fu, and Xing[3]. The result is a likelihood-based forecasting model capable of quantifying the transnational terrorist threat one state poses to another, even before any attacks have occurred between the two states. Specifically, we predict edges in the transnational terror network by substituting the network structure embedded in the recent patterns of transnational terrorism into the model that best predicted the network up to time t − 1. Thus, the predictive models for t are not based on the data from t. The result is a forecasting model that predicts edges that occur in the next time period (year) with probabilities orders of magnitude greater than those that do not occur. As such, our model provides forecasts of the locational dynamics of terrorist threats both before and after the first attacks have been realized. Our model lifts a major limitation of traditional approaches to forecasting transnational terrorist events and can provide early warnings of emerging threats.
Background
Though transnational terrorism has been a highly visible policy problem for the United States since the terrorist attacks of September 11, 2001, transnational terrorism is an older phenomena that, in many ways, came into its heyday with skyjacking, hostage taking, and bombing campaigns in the 1960’s and 1970’s. Quantitative research on transnational terrorist violence^{a} has focused largely on two related themes: the predictors of terrorist violence and trend analysis of the violence itself. The first thread of literature, developed largely in the field of political science, has linked higher probabilities of transnational terrorist violence to target states that have democratic governments[4], politically left governments[5], more veto-players in their governments[6], are perceived to be more likely to grant concessions to terrorists[7], and have further economic reach[8]. While this literature does much to shed light on the factors that may make a state more likely to suffer transnational terrorist attacks, it does little to provide forecasts of terrorist violence with any degree of precision. A second thread of literature has focused on trends in transnational terrorist violence itself. This literature, based at the intersection of political science and economics, has established that terrorist attacks exhibit cycling behavior[9], the number of terrorist attacks is decreasing but their lethality is increasing[10], substantial increases in levels of violence are usually unsustainable for the terrorist group[11], terrorist attacks are persistent following shocks in states suffering from low levels of terrorism (not for states suffering high levels of terrorism)[12], and terrorists tend to substitute targets when one type of target is hardened[13].
The literature that might help forecast terrorist events, however, has a major limitation: existent findings are either overly broad (i.e. democracies are more likely to be attacked by terrorists) or rely on voluminous attack data before trends can be identified and forecasts made. The lack of specificity from most statistical models of terrorist attacks is problematic from a policy perspective because, while it may warn a government that it is at elevated risk of terrorist attacks based on its attributes, it does little to inform the government about the source or timing of the threat. The trend analyses, while useful for predicting the ebb and flow of terrorist campaigns, are limited by not being able to make accurate predictions about the onset of hostilities. Furthermore, the literature on why discontented groups resort to terrorism[14, 15] is dedicated more to explaining the onset of terrorist campaigns than predicting such onset.
To date, the literature is moot in terms of statistical models designed not only to forecast attacks during terrorist campaigns, but to forecast emerging terrorist threats, and do so with a high degree of locational specificity: predicting not only when but from which country transnational terrorist attacks will emanate. Such a tool would provide insight from an academic perspective and prove useful from a policy perspective. It is with this aim that we develop a hybrid methodology from both deterministic and stochastic edge prediction techniques to predict the timing and locational dynamics of transnational terrorism.
Data
The data for our study are drawn from the “International Terrorism: Attributes of Terrorist Events” (ITERATE) dataset[1]. These data are well suited to our aims as they cover all transnational terrorist attacks over a 34 year period (1968–2002). The operational definition of transnational terrorism used for data collection is “the use, or threat of use, of anxiety-inducing, extra-normal violence for political purposes by any individual or group, whether acting for or in opposition to established governmental authority, when such action is intended to influence the attitudes and behavior of a target group wider than the immediate victims and when, through the nationality or foreign ties of its perpetrators, its location, the nature of its institutional or human victims, or the mechanics of its resolution, its ramifications transcend national boundaries.” ([1], p. 2) The ITERATE data are one of the most comprehensive and commonly used data sets on transnational terrorism (for example, see[4, 5, 8, 10, 11, 12, 16]).
The ITERATE data, among other variables, codes the known nationalities of the terrorists who participate in a given transnational attack and the location of the attack. From these variables, we create the network of transnational terrorist attacks by year. We code a directed edge as existing from country i to country j if a national of country i participates in a terrorist attack on location j; we call these terrorist edges. Note that many attacks, such as the September 11, 2001 attacks on the United States, are perpetrated by non-state actors (e.g., al-Qaeda). In such instances, we code a directed edge from every known nationality of the attackers involved in the attack implementation to the target vertex. One may object that transnational terrorists sometimes emigrate from their homelands, developing doctrine, training, and establishing support networks in states that are neither their home nor their target. However, when we consider the process of radicalization, this is less concerning. When a terrorist emigrates to develop their plans and capabilities, the process of radicalization proceeded the emigration and, thus, will typically take place in their home country. It is the case that some of the better-known terrorist masterminds spend substantial portions of their lives abroad, hopping from place to place, but this is more typical of senior group leadership and less typical of those who actually execute the attacks. As such, many of the globe-hoppers would not be included in the dataset anyway (if they did not participate in an identifiable way in the attack). Second, attempting to consider where a terrorist has spend their “important years” would introduce substantial coding problems. For example, many of the 9/11 hijackers received critical training (i.e. flight training) in the United States, but drawing a looping edge from the U.S. to the U.S. makes little substantive sense. Furthermore, data on where terrorists have spent their time prior to their attacks is not generally available and is prone to error and uncertainty; terrorists typically try to conceal their training camps and hideouts. As it stands, no information is available in our dataset beyond the known nationalities of attackers, and so we use that as a criteria for constructing the network.
To construct the network, we must also define the universe of possible terrorist edges in a given year, which requires a definition of membership in the international system. We rely principally on the definition of the state system provided by the Correlates of War Project, which keeps a database of all countries that belong to the international community in a given year.^{b} We augment membership in the international community by adding a few non-state actors that have been either the source or the target of transnational terrorism (e.g. Palestine and the United Nations). Though such entities are not technically countries, including them in the network is preferable to excluding them because contested territories are important producers of transnational terrorism and not including international governmental organizations would misclassify the target of the attack (i.e. where it occurred rather than who was targeted).
All together, we produce a network with a median of 175 vertices over the time span that we study. A feature of these data that is somewhat atypical in network analysis is that self-ties are present. It is common for terrorists from state i to commit an attack in state i. While we include these “loops” in our analysis, it is important to point out that all of these loops are affiliated in some way with a transnational terrorist incident. The ITERATE data do not code domestic terrorist attacks and, as such, loops represent acts in which a native of the target country collaborates with foreign terrorists to launch an attack.
These two results, (1) that many edges represent innovations with respect to the recent past and (2) the network exhibits significant transitivity, indicate that proximity-based link prediction should be a fruitful exercise on the transnational terrorism network. The persistence of innovation means that any information that can be leveraged about the indirect ties in the network will be quite valuable. The transitivity indicates that indirect ties will have predictive power with respect to edge formation.
Why is transnational terrorism transitive?
It is not immediately intuitive why the network of transnational terrorist attacks would exhibit the high degree of transitivity we observe with the CUG test. Conflictual international networks, such as international war[19], exhibit substantial intransitivity; whereas transitivity is commonly a feature of cooperative international networks (e.g. military alliances)[20, 21].
When approaching this question theoretically, it is useful to distinguish between two common types of terrorist groups by motivation: ethno-nationalist groups and religious/ideological groups. Ethno-nationalist groups have specific goals of creating a state for their ethnic group or liberating their nation from occupation (real or perceived) and, as such, their attacks tend to be confined to only one target. Examples of such groups include the Provisional Irish Republican Army (PIRA) and the Kurdistan Workers’ Party (PKK). For ethno-nationalist groups, terrorist violence is tied directly to the attainment of their nationalistic goals. Conversely, religious/ideological groups are organized around a religious or political/ideological ideal and tend to lack a clear policy objective.^{c} However, such groups tend to have broader, multinational, support bases and to attack targets in a number of countries. They tend to target countries that exhibit religious/ideological cultures that are counter to the groups’ ideals. Groups such as al-Qaeda and the Red Army Faction fall into this category.
A second situation that can give rise to transitivity in the network, for either ethno-nationalist or religious/ideological groups, is an environment with multiple terrorist groups. For example, extreme right and extreme left groups may be active in the same region and their overlapping attacks may form transitive patters. This two-group process is illustrated in the right column of Figure3. Furthermore, a multi-group region need not be populated with groups of opposing ideals in order to form transitive triads. Bapat[22] provides an explanation for why infighting between groups with a common opponent is common, especially as peace processes progress. When a target state makes a move towards peace with its attackers, that move will usually involve active negotiations with one or several groups. In order to get their desired concessions, the negotiating group must moderate its behavior. This, however, is often not welcome by other groups or by radicals within the negotiating group. If the negotiating group is successful, it will, at best, seize power away from rival groups or, at worst, seize power away from rivals while negotiating a settlement that is unacceptable to a broad swath of rivals and radicals; either way, rival groups have an incentive to resist the change and radicals within the negotiating group have an incentive to form splinter groups. Resisting groups have been known to launch spoiler campaigns agains the target state (attacks designed to provoke the target state and make peace less likely) or launch attacks directly on the negotiating group. At the same time, the negotiating group needs a monopoly on terrorist violence in order to be a reliable negotiating partner for the government, so it has an incentive to crack down on dissidents and rivals.
Method
Our method of forecasting is based on a probabilistic modeling framework, and incorporates proximity measures from a deterministic edge prediction method. For the probabilistic base of our method, we use the temporal exponential random graph modeling (TERGM) framework developed by Hanneke, Fu, and Xing[3]. To define the specific TERGMs, we incorporate vertex-similarity measures drawn from Liben-Nowell and Kleinberg[2], who originally used those measures in a deterministic manner. We first review the TERGM approach to modeling networks, then we describe the vertex-similarity measures and how we incorporate them into the TERGM modeling framework.
where$\mathit{\theta}\in {\mathbb{R}}^{p}$ is the parameter vector, Γ:$N\to {\mathbb{R}}^{p}$ is a vector of statistics that are computed on the network, and the summation in the denominator is a normalizing constant computed on the support of N (denoted$\mathcal{N}$). This model is flexible in that Γ can be specified to capture virtually any form of interdependence among the edges in the networks, as well as dependence of the edges on exogenous features.
Hanneke, Fu, and Xing[3] extended the ERGM to model a network observed at numerous discrete time points, which extends the first-order dependence of the original model formulation[25]. This is accomplished mathematically by including past realizations of N in the Γ that defines the ERG distribution for the current network. The network is observed in T discrete time periods. Let N^{ t } be the observed network at time t. Temporal interdependence of the networks can be built into the model by conditioning N^{ t } on K previous realizations of the network.
Recall that the denominator in Equation 1 is a normalizing constant (i.e., a partition function). We update the notation in 2 to reflect this property. The likelihood function is defined as$\prod _{t=K+1}^{T}\mathcal{P}\left({N}^{t}\right|K,\mathit{\theta})$.^{d} In our implementation, a new θ is estimated for each t (i.e., θ^{ t }). We allow parameters to vary by period due to temporal heterogeneity in the network structure, which is indicated by the considerable decrease in the density of the network over time and is visible in Figure1.
In what can safely be called the foundational work on edge prediction in complex networks, Liben-Nowell and Kleinberg[2] capitalize the insight that vertices close or similar to each other in a network are likely to link in the future. They describe multiple measures of “proximity” in a network. Each measure of proximity results in a score δ(i,j) for each dyad of vertices ij in the network. These scores are then computed on a training network defined over an interval of the past. Dyads are then ranked with respect to these scores. For prediction, the potential new edges are constrained to be those meeting a certain degree threshold in the training network. The subset of dyads defined on this network are then ranked with respect to their proximity scores and dyads that have high δ are predicted to be edges in the next time interval. Each proximity measure is evaluated with respect to its predictive performance.
If states i or j were not in the international system during the period taken as the training network interval [t_{0},t−1], then we set$\delta {(i,j)}^{{t}_{0},t-1}$ = 0. Considering Figure1, there appears to be significant dependence of the current network on the network from t − 1 and that in [t − 5,t − 2]. We therefore perform our analyses setting t_{0} at t − 1 and t − 5.
- 1.
Flow. This measure generalizes preferential attachment [2] to the directed case. Preferential attachment is implemented as a measure of proximity by Liben-Nowell [2] as δ(i,j) = k _{ i } k _{ j }, where k is the degree (i.e., the number of edges) of a given vertex. To take advantage of the direction of the ties, we conceive of a process whereby an attack from i to j is likely if i sends many attacks and/or j receives many attacks. In other words, we posit that frequent attackers are close to regular targets in the network. The measure of flow is $\delta (i,j)={k}_{i}^{o}{k}_{j}^{i}$, where k ^{ o } and k ^{ i } are the out and in-degrees respectively.
- 2.
CTarget. The number of common targets shared by two countries: $\delta (i,j)=\sum _{h}{N}_{\mathit{\text{ih}}}{N}_{\mathit{\text{jh}}}$.
- 3.
CAttacker. The number of common attackers shared by two countries: $\delta (i,j)=\sum _{h}{N}_{\mathit{\text{hi}}}{N}_{\mathit{\text{hj}}}$
- 4.
JacSim. The Jaccard similarity between two countries is δ(i,j) = [CTarget + CAttacker] / [k _{ i }+ k _{ j }], which normalizes the measure of common neighbors by the total number of neighbors of the vertices in the dyad.
- 5.
AASim. The Adamic/Adar similarity adjusts the measure of common neighbors for the rarity of the neighbors to which the two countries tie. This measure is defined as $\delta (i,j)=\sum _{h}{\left[ln\left({k}_{h}\right)\right]}^{-1}({N}_{\mathit{\text{ih}}}{N}_{\mathit{\text{jh}}}+{N}_{\mathit{\text{hi}}}{N}_{\mathit{\text{ji}}})$.
- 6.
SameCom. Common community membership. We partition the countries into communities using the random walk modularity optimization algorithm “Walktrap” [26] and create an indicator, δ(i j) = 1(c _{ i }== c _{ j }), of whether i and j are members of the same community.
- 7.
Distance. Lastly, we include the minimum path length between i and j. We set δ(i,j) equal to the number of countries in the network plus one if there is no path from i to j.
In each model we include a count of the number of edges in the network to model the network’s density. In addition to the proximity measures, and following Hanneke, Fu, and Xing[3], we include a memory term (PrevAttack) to capture persistence in the ties between the training network and the current network. The memory term at time t is specified as$\sum _{\mathit{\text{ij}}}{N}_{\mathit{\text{ij}}}^{t}{N}_{\mathit{\text{ij}}}^{{t}_{0},t-1}+(1-{N}_{\mathit{\text{ij}}}^{t})(1-{N}_{\mathit{\text{ij}}}^{{t}_{0},t-1})$. We try each statistic computed on the networks over the interval t − 1,t − 1] and t − 5,t − 1]. In the interest of comparing the performance of models on edges that did not occur in the past 10 years, we start our analysis at 1980 and go through the end of the dataset in 2002. Each model contains the edges term and some subset, including the empty set, of the memory and proximity terms, at both the one and five year intervals. The memory term and each of the proximity terms is (a) included computed on the one year training interval, (b) included computed on the five year training interval, and (c) excluded from the model. This leads to a total of 3^{8} = 6,561 models estimated at each t
The forecast model for t is selected as the best performing model up to t − 1. Performance is judged based on the predictive log score (i.e., the forecast log-likelihood)[27]. By using the predictive log score, in expectation, we use the model with the minimum Kullback-Leibler divergence from the actual model that generated the data[27]. We use θ^{t−1} to perform the forecast of N^{ t }, which was estimated to fit N^{t−1} based on${N}^{{t}_{0}-1,t-2}$. Thus, it is a true forecast in that the TERGM used to predict N^{ t } has only been trained on the series of networks up to t − 1.
- 1.
Estimate each of the 6,561 forecasting models for each time point from 1980 up to the previous year. Denote the structural measures in model M as Γ _{ M }. Let ${\mathit{\theta}}_{M}^{t}$ be the parameters estimated on N ^{ t } using Γ _{ M }.
- 2.Select as the forecasting model ( M ^{∗}) for time t to be that model maximizing$\sum _{i=1981}^{t-1}ln\left[\mathcal{P}({N}^{i}|{\mathit{\theta}}_{M}^{i-1},{\mathbf{\Gamma}}_{M})\right].$
- 3.Forecast the next network from the distribution$\frac{exp\{{\left[{\mathit{\theta}}_{{M}^{\ast}}^{t-1}\right]}^{\prime}\phantom{\rule{0.3em}{0ex}}{\mathbf{\Gamma}}_{{M}^{\ast}}(N,{N}^{{t}_{0},t-1})\}}{C\left({\mathit{\theta}}_{{M}^{\ast}}^{t-1}\right)}.$
- 4.
Draw many forecast networks from the distribution in item 3 and compute the mean edge value in order to estimate the probability of any particular edge.
We apply this algorithm to all 23 years of the transnational terrorist network under consideration.
Results
There are a number of questions to be asked of our results. First, what is the overall performance of our approach to forecasting transnational terrorism? Second, does our approach offer leverage in predicting innovations in transnational terrorist relationships? Third, can we see any patterns in the proximity and memory features that predict transnational terrorism? We address these questions in turn.
Case test: The Saudi link to the U.S. in 2001
The terror attacks of September 11, 2001 are the most spectacular and terrible the world has yet seen. They were also unexpected by policy and intelligence analysts. Among the surprises of the 9/11 attacks was the fact that 15 of the 19 hijackers were Saudi; indeed, it was the first time a Saudi citizen had committed any sort of attack on U.S. soil in almost three decades. As a test case, we examine what information our forecasting model provides about that 9/11 link from Saudi Arabia to the U.S.
Top ten predicted sources of terrorism against targets inside the U.S., 2001
Rank | Country | P(Attack) |
---|---|---|
1 | Algeria | 0.126 |
2 | Pakistan | 0.055 |
3 | Iraq | 0.044 |
4 | Jordan | 0.037 |
5 | Cuba | 0.037 |
6 | Canada | 0.029 |
7 | Romania | 0.024 |
8 | Saudi Arabia | 0.012 |
9 | Egypt | 0.011 |
10 | Iran | 0.011 |
Predictive model for 2001
δ | t _{0} | θ | δ %tile* |
---|---|---|---|
PrevAttack | 1996 | 1.64 | 0 |
Flow | 1996 | 0.027 | 99.99 |
CAttacker | 1996 | 0.24 | 98.46 |
AASim | 2000 | 0.5 | 0 |
SameComm | 2000 | 0.441 | 0 |
Distance | 1996 | 4.07 | 98.89 |
Conclusion
Our study of the transnational terrorist network makes at least three major contributions. First, we contribute to the literature on edge forecasting in complex networks. We integrate deterministic proximity-based forecasting into the probabilistic TERGM modeling of the evolution of a network based on its own topography. This approach can be applied to the edge prediction problem in many areas. This general method may prove useful for predicting the occurrence of edges in any variety of other networks such as international conflict (war), scientific collaboration and friendship.
We contributed to the state of knowledge about transnational terrorism by identifying that (1) there is an even mix of memory and innovation in the transnational terrorism network and (2) the network exhibits substantial transitivity. The transitivity we observe is likely due to to economic, political, linguistic, and religious clustering that are subsumed under country labels. In other words, the way in which we define the vertices in the networks acts as a catch-all for the features likely to drive terrorism. Future research should address what specific features of countries predict terrorist link formation.
Lastly, but perhaps most importantly, we have advanced terrorism forecasting models in two critical directions. Our approach provides the necessary source-target specificity required to be useful for protecting the target and addressing the source. Second, by leveraging the information on indirect ties in the network, our method is able to predict the occurrence of new terrorist edges. The ability to predict edge innovation is critical from a policy perspective because early warning is essential for the allocation of security resources that can, potentially, save lives.
Endnotes
^{a}It is worth noting that there is a deep literature on psychological traits that make an individual more likely to become a terrorist and on the psychological group dynamics that affect a group’s cohesion, but we do not consider this literature extensively here because its focus relates to individual behaviors rather than the amount of violence states suffer at the hands of terrorists. See[14, 31] for reviews of this literature.
^{b}These data are freely available athttp://www.correlatesofwar.org/.
^{c}They tend to at least lack realistic policy objectives, though they may have stated objectives such as the imposition of global Islamic law or communism.
^{d}Note that the computation of the likelihood requires the omission of the first K networks. Hanneke, Fu, and Xing[3] point out that one could also specify a separate probability model for these networks, but it is unclear what benefit would come of such an exercise, since this convenience model would, by construction, be misspecified.
Notes
Acknowledgements
This work was supported, in part, by a research grant from the College of Social and Behavioral Sciences, University of Massachusetts Amherst and by a grant from the University of North Carolina at Chapel Hill’s University Research Council.
Supplementary material
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