Abstract
In this chapter, we introduce two innovative methodologies that were first used in the field of criminology and have then been applied to systematically analyze terrorism over time. The first innovation, group-based trajectory analysis, presents the big picture of terrorism by grouping countries or terrorist organizations with similar attack patterns. The second innovation, series hazard modeling, drills down to specific cases (e.g., countries, organizations, or movements) to estimate changes in the hazard of another attack based on changes in independent variables, such as government interventions or other potential turning points. These two approaches help us understand longitudinal terrorism patterns in different way. Each method has its unique strengths and provides answers to different questions regarding terrorism trends.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In order to consider an incident for inclusion in the GTD, all three of the following attributes must be present: (1) The incident must be intentional – the result of a conscious calculation on the part of a perpetrator. (2) The incident must entail some level of violence or threat of violence – including property violence, as well as violence against people. (3) The perpetrators of the incidents must be sub-national actors. This database does not include acts of state terrorism. In addition, at least two of the following three criteria must be present for an incident to be included in the GTD: Criterion 1: The act must be aimed at attaining a political, economic, religious, or social goal. In terms of economic goals, the exclusive pursuit of profit does not satisfy this criterion. It must involve the pursuit of more profound, systemic economic change. Criterion 2: There must be evidence of an intention to coerce, intimidate, or convey some other message to a larger audience (or audiences) than the immediate victims. It is the act taken as a totality that is considered, irrespective if every individual involved in carrying out the act was aware of this intention. As long as any of the planners or decision-makers behind the attack intended to coerce, intimidate or publicize, the intentionality criterion is met. Criterion 3: The action must be outside the context of legitimate warfare activities. That is, the act must be outside the parameters permitted by international humanitarian law (particularly the prohibition against deliberately targeting civilians or noncombatants).
- 2.
The term “hot spot” tends to be used to describe a high concentration of social problems like crime in a very small number of places (see Sherman & Weisburd, 1995). In this case, LaFree, Morris, et al. (2009) follow the same fashion and refer the small number countries with a large share of terrorist attacks as terrorist hot spots.
- 3.
The term terrorist “organization” and terrorist “group” tend to be used interchangeably. In this chapter, however, we want to avoid confusion between trajectory group and terrorist group and use the term “organization” when we talk about individual terrorist groups.
- 4.
In this study, we use macro Proc Traj, a SAS procedure, to execute the analysis (see Jones et al., 2001). Other statistical programs can also be used for GBTA including M Plus©. More information about Proc Traj, programming examples, and documentation can be found at the following website http://www.andrew.cmu.edu/user/bjones/index.html.
- 5.
Intermittency “refers to episodes of inactivity in a criminal career” (Nagin, 2005, page 34). The observation of zero activity can be a result of two possibilities: the true lack of activity or the lack of opportunity for such activity for the given time period. The intermittency parameter is added in the model to account for both situations.
- 6.
In our study, the only trajectory group affected by the truncation practice is the 1980s Boom. When plotting the projected trajectories and the actual values, it is clear that the projections and actual values almost totally overlap (except for 1980s Boom and a very minor deviation of the 1990s Boom) over the 35 years.
- 7.
- 8.
The exact polynomial orders of each trajectory in the final solution are as following Sporadic (quadratic), twenty-first Century (cubic), 1970s Onset (quartic), 1990s Onset (cubic), and 1980s Onset (cubic).
- 9.
The process of executing GBTA is computationally intensive and could take several iterations before reaching the final convergence. Thus, start values can be added to the program to help Proc Traj identify the solution more efficiently. Additionally, specifying start values can help avoid finding solution with local maximum likelihood rather than global maximum likelihood value. Due to the simplicity of this example, we did not specify start values in our program. For readers who wish to understand more about start values and examples in programming, please refer to http://www.andrew.cmu.edu/user/bjones/example.html.
- 10.
The Proc Traj program also produces a set of predicted number of attacks based on the estimated parameters for each trajectory group. Others have found it useful to produce both the projected trajectories and the average number of events to represent each trajectory group.
- 11.
In fact, in order to avoid bias in the standard errors, dependency between events should be modeled to establish conditional independence (Dugan, 2011a).
- 12.
The self-excitement model is designed to weigh more recent events heavier than earlier events using an exponential function that eventually converges to zero for the earliest events, incorporating the assumption that “every incident tends to be forgotten eventually” (Holden, 1986: 888).
- 13.
While the month was used in this example, the program can be easily modified to use a more refined unit, such as day.
- 14.
The original coders of the GTD define success by the details of the terrorist event. If a bomb exploded, then it was considered successful, even if the larger intent of the organization was not achieved (Dugan et al., 2005).
- 15.
The post-arrest downward trend in this figure makes the reason that the main effect was statistically insignificant more obvious. If we extend the after-arrest line toward zero months, the hazard ratio would be very close to one when it crosses the zero month (not shown in graph).
References
Allison, P. D. (1995). Survival analysis using the SAS system: A practical guide. Cary: SAS Institute Inc.
Alt, J. E., King, G., & Signorino, C. S. (2000). Aggregation among binary, count, and duration models: Estimating the same quantities from different levels of data. Political Analysis, 9(1), 21–44.
Bennett, A., & Elman, C. (2007). Case study methods in the international relations subfield. Comparative Political Studies, 40(2), 170–195.
Blokland, A. A. J., Nagin, D. S., & Nieuwbeerta, P. (2005). Life span offending trajectories of a Dutch conviction cohort. Criminology, 43, 919–954.
Brandt, P. T., & Williams, J. T. (2007). Multiple time series models. Thousand Oaks: Sage Publications, Inc.
Bushway, S. D., Sweeten, G., & Nieuwbeerta, P. (2009). Measuring long term individual trajectories of offending using multiple methods. Journal of Quantitative Criminology, 25(3), 259–286.
Bushway, S. D., Thornberry, T. P., & Krohn, M. D. (2003). Desistance as a developmental process: A comparison of static and dynamic approaches. Journal of Quantitative Criminology, 19(2), 129–153.
Callaway, R., & Harrelson-Stephens, J. (2006). Toward a theory of terrorism: Human security as a determinant of terrorism. Studies in Conflict and Terrorism, 29(7), 679–702.
Cordes, B. (2001). When terrorist do the talking: Reflections on terrorist literature. In D. C. Rapoport (Ed.), Inside terrorism organizations (pp. 150–171). London: Frank Cass Publishers.
Crenshaw, M. (2001). Theories of terrorism: Instrumental and organizational approaches. In D. C. Rapoport (Ed.), Inside terrorism organizations (pp. 13–29). London: Frank Cass Publishers.
Cronin, A. K. (2006). How al-Qaida ends: The decline and demise of terrorist groups. International Security, 31(1), 7–48.
D’Alessio, S. J., & Stolzenberg, L. (1995). The impact of sentencing guidelines on jail incarceration in Minnesota. Criminology, 33(2), 283–302.
Dugan, L. (2011a). The series hazard model: An alternative to time series for event data. Journal of Quantitative Criminology.
Dugan, L. (2011b). The making of the Global Terrorism Database and its applicability to studying the lifecycles of terrorist organizations. In D. Gadd, S. Karstedt, & S. Messner (Eds.), The sage handbook of criminological research methods.
Dugan, L., Huang, J., LaFree, G., & McCauley, C. (2008). Sudden desistance from terrorism: The American Secret Army for the Liberation of Armenia and the Justice Commandos of the Armenian Genocide. Dynamics of Asymmetric Conflict, 1(3), 231–249.
Dugan, L., Lafree, G. L., Cragin, K., & Kasupski, A. (2008). Building and analyzing an open source comprehensive database on global terrorist events (DOJ Publication No. 223287). Washington: U.S. Government Printing Office.
Dugan, L., LaFree, G., & Miller, E. (2011). Using rational choice to better identify the most threatening terrorist organizations. Working paper. The University of Maryland.
Dugan, L., LaFree, G., & Piquero, A. R. (2005). Testing a rational choice model of airline hijackings. Criminology, 43(4), 1031–1066.
Eggleston, E. P., Laub, J. H., & Sampson, R. J. (2004). Methodological sensitivities to latent class analysis of long-term criminal trajectories. Journal of Quantitative Criminology, 20(1), 1–26.
Enders, W., & Sandler, T. (1993). The effectiveness of antiterrorism policies: A vector-autoregression-intervention analysis. American Political Science Review, 87(4), 829–844.
Enders, W., & Sandler, T. (2006). The political economy of terrorism. New York: Cambridge University Press.
Freeman, J. R. (1989). Systematic sampling: Temporal aggregation, and the study of political relationships. Political Analysis, 1(1), 61–98.
Griffiths, E., & Chavez, J. M. (2004). Communities, street guns, and homicide trajectories in Chicago, 1980–1995: Merging methods for examining homicide trends across space and time. Criminology, 42(4), 941–978.
Holden, R. T. (1986). The contagiousness of aircraft hijacking. American Journal of Sociology, 91(4), 874–904.
Ihrie, G. (2010). Functional data analysis. Unpublished manuscript.
Jackson, B., Baker, J. C., Cragin, K., Parachini, J., Trujillo, H. R., & Chalk, P. (2005). Aptitude for destruction volume 2: Case studies of organizational learning in five terrorist groups. Santa Monica: RAND Corporation.
Jones, B. L., Nagin, D. S., and Roeder, K. (2001). A SAS procedure based on mixture models for estimating developmental trajectories. Sociol. Meth. Res. 29, 374–393.
Jones, S. G., & Libicki, M. C. (2008). How terrorist groups end: Lessens for countering al Qa’ida. Santa Monica: RAND Corporation.
Jung, T., & Wickrama, K. A. S. (2008). An introduction to latent class growth analysis and growth mixture modeling. Social and Personality Psychology Compass, 2(1), 302–317.
Kruger, A. B., & Maleckova, J. (2003). Education, poverty, and terrorism: Is there a causal connection? Journal of Economic Perspectives, 17(4), 119–144.
LaFree, G., & Dugan, L. (2007). Introducing the Global Terrorism Database. Terrorism and Political Violence, 19(2), 181–204.
LaFree, G., Dugan, L., Fogg, H., & Scott, J. (2006). Building a Global Terrorism Database (DOJ Publication No. 214260). Washington: U.S. Givernment Printing Office.
LaFree, G., Dugan, L., & Korte, R. (2009). The impact of British counterterrorist strategies on political violence in Northern Ireland: Comparing deterrence and backlash models. Criminology, 47(1), 17–45.
LaFree, G., Mazerolle, L., Denning, R., Miller, E., White, G., & Yang, S. -M. (2011). Modeling the Effectiveness of Counter-Terrorism Strategies in Indonesia, the Philippines and Thailand. Final Report. National Consortium for the Study of Terrorism and Responses to Terrorism (U.S.) and Centre of Excellence in Policing and Security (Australia).
LaFree, G., Morris, N. A., & Dugan, L. (2009). Cross-national patterns of terrorism: Comparing trajectories for total attributed and fatal attacks, 1970–2006. British Journal of Criminology, 50(4), 622–649.
Lafree, G., Morris, N. A., Dugan, L., & Fahey, S. (2006). Identifying cross-national global terrorist hot spots. In J. Vicktoroff (Ed.), Tangled roots: Social and psychological factors in the genesis of terrorism (pp. 98–114). Amsterdam: Ios Press.
LaFree, G., Yang, S.-M., & Crenshaw, M. (2009). Trajectories of terrorism: Attack patterns of foreign groups that have targeted the United States, 1970–2004. Criminology and Public Policy, 8(3), 445–473.
LaFree, G., Yang, S.-M., & Crenshaw, M. (2010). International cooperation, not unilateral policies may be the best counterterrorist strategy. In N. A. Frost, J. D. Freilich, & T. R. Clear (Eds.), Contemporary issues in criminal justice policy: Policy proposals from the American Society of Criminology Conference (pp. 121–128). Belmont: Cengage/Wadsworth.
Laub, J. H. (2006). Edwin H. Sutherland and the Michael-Adler report: Searching for the soul of criminology seventy years later. Criminology, 44(2), 235–257.
Lewis-Beck, M. S. (1986). Interrupted time series. In W. D. Berry & M. S. Lewis-Beck (Eds.), New tools for social scientists (pp. 209–240). Beverly Hills: Sage Publications.
Li, Q. (2005). Does democracy promote or reduce transnational terrorist incidents? Journal of Conflict Resolution, 49(2), 278–297.
Li, Q., & Schaub, D. (2004). Economic globalization and transnational terrorism: A pooled time-series analysis. Journal of Conflict Resolution, 48(2), 23–58.
Lum, C. (2009). Theoretical and methodological innovations in terrorism research: A response to LaFree, Yang and Crenshaw. In N. A. Frost, J. D. Freilich, & T. R. Clear (Eds.), Contemporary issues in criminal justice policy: Policy proposals from the American Society of Criminology Conference (pp. 133–138). Belmont: Cengage/Wadsworth.
Lum, C., Kennedy, L., & Sherley, A. (2006). Are counter-terrorism strategies effective? The results of the Campbell systematic review on counter-terrorism evaluation research. Journal of Experimental Criminology, 2(4), 489–516.
Lum, C., & Yang, S.-M. (2005). Why do evaluation researchers in crime and justice choose non-experimental methods? Journal of Experimental Criminology, 1(2), 191–213.
McCauley, C. (2001). What do terrorists want? Psychological Science Agenda, 14(6), 5.
McCormick, G. H. (2001). The shining path and Peruvian terrorism. In D. C. Rapoport (Ed.), Inside terrorist organizations (pp. 109–128). London: Frank Cass Publishers.
McDowall, D., Lizotte, A. J., & Wiersema, B. (1991). General deterrence through civilian gun ownership: An evaluation of the quasi-experimental evidence. Criminology, 29(4), 541–560.
Miller, E. (2009). Patterns of decline among terrorist movements. Presented at the American Society of Criminology Conference, Philadelphia.
Moffitt, T. E. (2006). A review of research on the taxonomy of life-course persistent and adolescence-limited offender. In F. T. Cullen, J. P. Wright, & M. Coleman (Eds.), Taking stock: The status of criminological theory (pp. 277–311). New Brunswick: Transaction Publishers.
Morris, N., & Slocum, L. (In progress). Estimating county level terrorism trends using group-based trajectory analysis: A comparison of latent class growth analysis and general mixture modeling.
Muthén, B. (2001). Second general structural equation modeling with a combination of categorical and continuous latent variables: New opportunities for latent class-latent growth modeling. In L. M. Collins & A. G. Sayers (Eds.), New methods for the analysis of change (pp. 289–322). Washington: American Psychological Association.
Nagin, D. S. (1999). Analyzing developmental trajectories: A semi-parametric, group-based approach. Psychological Methods, 4(2), 139–157.
Nagin, D. S. (2005). Group-based modeling of development. Cambridge: Harvard University Press.
Nagin, D. S., Farrington, D. P., & Moffit, T. E. (1995). Life-course trajectories of different types of offenders. Criminology, 33(1), 111–139.
Nagin, D. S., & Land, K. C. (1993). Age, criminal careers, and population heterogeneity: Specification and estimation of a nonparametric, mixed Poisson model. Criminology, 31(3), 327–362.
Nagin, D. S., & Tremblay, R. E. (1999). Trajectories of boys’ physical aggression, opposition, and hyperactivity on the path to physically violent and nonviolent juvenile delinquency. Child Development, 70(5), 1181–1196.
Nagin, D. S., & Tremblay, R. E. (2001). Parental and early childhood predictors of persistent physical aggression in boys from kindergarten to high school. Archives of General Psychiatry, 58(4), 389–394.
Odell, J. S. (2004). Case study methods in international political economy. In D. F. Sprinz & Y. Wolinsky-Nahmias (Eds.), Models, numbers and cases: Methods for studying international relations (pp. 56–80). Ann Arbor: University of Michigan Press.
Piazza, J. A. (2006). Rooted in poverty? Terrorism, poor economic development, and social cleavages. Terrorism and Political Violence, 18(1), 159–177.
Rapoport, D. C. (1992). Terrorism. In M. Hawkesworth & M. Kogan (Eds.), Routledge encyclopedia of government and politics (Vol. 2). London: Routledge.
Rapoport, D. C. (2004). The four waves of modern terrorism. In A. K. Cronin & J. Ludes (Eds.), The campaign against international terrorism (pp. 46–73). Washington: Georgetown University Press.
Raudenbush, S. (2001). Toward a coherent framework for comparing trajectories of individual change. In L. M. Collins & A. G. Sayers (Eds.), New methods for the analysis of change (pp. 35–63). Washington: American Psychological Association.
Roeder, K., Lynch, K. G., & Nagin, D. S. (1999). Modeling uncertainty in latent class membership: A case study in criminology. Journal of the American Statistical Association, 94(447), 766–776.
Shellman, S. M. (2004a). Time series intervals and statistical inference: The effects of temporal aggregation on event data analysis. Political Analysis, 12(1), 97–104.
Shellman, S. M. (2004b). Measuring the intensity of intranational political events data: Two interval-like scales. International Interactions, 30(2), 109–141.
Sherman, L. W., & Weisburd, D. (1995). General deterrent effects of police patrol in crime “Hot Spots”: A randomized, controlled trial. Justice Quarterly, 12(4), 625–648.
Skardhamar, T. (2010). Distinguishing facts and artifacts in group-based modeling. Criminology, 48(1), 295–320.
Soule, J. W. (1989). Problems in applying counter terrorism to prevent terrorism: Two decades of violence in Northern Ireland reconsidered. Terrorism, 12(1), 31–46.
Sweeten, G. (2006). Causal inference with group-based trajectories and propensity score matching: Is high school dropout a turning point? Unpublished doctoral dissertation, University of Maryland, College Park.
United States Institute of Peace. (1999). How terrorism ends. Special Report, No. 48. Washington: United States Institute for Peace.
Weisburd, D. L., Bushway, S., Lum, C., & Yang, S.-M. (2004). Trajectories of crime at places: A longitudinal study of street segments in the city of Seattle. Criminology, 42(2), 283–321.
Weisburd, D. L., Groff, E., & Yang, S. -M. (2010). Understanding Developmental Crime Trajectories at Places: Social Disorganization and Opportunity Perspectives at Micro Units of Geography. Final Report. National Institute of Justice Grant. Number 2005-IJ-CX-0006.
Weisburd, D. L., Morris, N., & Groff, E. R. (2009). Hot spots of juvenile crime: A longitudinal study of street segments in Seattle, Washington. Journal of Quantitative Criminology, 25(4), 443–467.
Wilson, J. Q., & Kelling, G. L. (1982). Broken windows: The police and neighborhood safety. The Atlantic Monthly, 249(3), 29–38.
Yang, S.-M. (2010). Assessing the spatial-temporal relationship between disorder and violence. Journal of Quantitative Criminology, 26(1), 139–163.
Yang, S. -M., & LaFree, G. (2011). Trajectories and geospatial patterns (Chapter 4). In G. LaFree, L. Mazerolle, R. Denning, E. Miller, G. White, & S.-M. Yang (Eds.), Modeling the effectiveness of counter-terrorism strategies in Indonesia, the Phillipines and Thailand. A final report for the National Consortium for the Study of Terrorism and Responses to Terrorism (U.S.) and Centre of Excellence in Policing and Security (Australia).
Young, J., & Dugan, L. (2011). Veto players and terror. Journal of Peace Research, 48(1), 19–33.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Dugan, L., Yang, SM. (2012). Introducing Group-Based Trajectory Analysis and Series Hazard Modeling: Two Innovative Methods to Systematically Examine Terrorism Over Time. In: Lum, C., Kennedy, L. (eds) Evidence-Based Counterterrorism Policy. Springer Series on Evidence-Based Crime Policy, vol 3. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0953-3_6
Download citation
DOI: https://doi.org/10.1007/978-1-4614-0953-3_6
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-0952-6
Online ISBN: 978-1-4614-0953-3
eBook Packages: Humanities, Social Sciences and LawSocial Sciences (R0)