Skip to main content
SpringerLink
Log in

Replicating Group-Based Trajectory Models of Crime at Micro-Places in Albany, NY

  • Original Paper
  • Published:
Journal of Quantitative Criminology Aims and scope Submit manuscript

Abstract

Objectives

Replicate two previous studies of temporal crime trends at the street block level. We replicate the general approach of group-based trajectory modelling of crimes at micro-places originally taken by Weisburd et al. (Criminology 42(2):283–322, 2004) and replicated by Curman et al. (J Quant Criminol 31(1):127–147, 2014). We examine patterns in a city of a different character (Albany, NY) than those previously examined (Seattle and Vancouver) and so contribute to the generalizability of previous findings.

Methods

Crimes between 2000 and 2013 were used to identify different trajectory groups at street segments and intersections. Zero-inflated Poisson regression models are used to identify the trajectories. Pin maps, Ripley’s K and neighbor transition matrices are used to show the spatial patterning of the trajectory groups.

Results

The trajectory solution with eight classes is selected based on several model selection criteria. The trajectory of each those groups follow the overall citywide decline, and are only separated by the mean level of crime. Spatial analysis shows that higher crime trajectory groups are more likely to be nearby one another, potentially suggesting a diffusion process.

Conclusions

Our work adds additional support to that of others who have found tight coupling of crime at micro-places. We find that the clustering of trajectories identified a set of street units that disproportionately contributed to the total level of crime citywide in Albany, consistent with previous research. However, the temporal trends over time in Albany differed from those exhibited in previous work in Seattle but were consistent with patterns in Vancouver.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Notes

  1. The impetus for our analysis was an effort, in collaboration with the Albany Police Department, to more strategically focus proactive policing, for which the identification of stable high-crime locations was necessary.

  2. Another approach distinct from growth mixture models is to use k-means clustering with a specialized distance matrix for the time series observations (Genolini and Falissard 2010). Curman et al. (2014) provide a comparison of this approach with the more typical growth mixture modelling approach of Proc Traj.

  3. In Seattle, 19 percent of the incident records identified the location as an intersection (Weisburd et al. 2004: 291). In Vancouver, 25 percent of the incidents were recorded as occurring at an intersection (Curman et al. 2014: fn. 2).

  4. This file is available from the New York State GIS Clearinghouse, https://gis.ny.gov/.

  5. The python library NetworkX and the components.connected function was used to calculate the transitive closure (Hagberg et al. 2008).

  6. This presumes that each would converge to the same results. Nielsen et al. (2013) suggests that their crimCV implementation has a more robust search for starting parameters to prevent pre-mature optimization as compared to Proc Traj.

  7. Solutions with 10 and 11 groups were estimated reducing the search for the initial starting parameters (from the default of 20 to only 10). In each of these solutions, the AIC and BIC values were higher than the 8 group solution. Not all of the leave-one-out models converged, so there are no available cross validation statistics to compare for the 10 and 11 group solution.

  8. Inasmuch as some types of crime are more suppressible through police presence than others are, decisions about targeted deployment would in addition take into account the types of crime that comprise the counts in these high-crime micro-places.

  9. Synonymous trajectory models were fit for Part 1 and Part 2 crimes separately. The results are very similar, and there is a large amount of overlap between the trajectory groups, e.g. a high Part 1 crime location also tends to be a high Part 2 crime location. These results are presented in Appendix 1.

  10. Applications of the randomly relabeling approach to calculating point pattern statistics appear to be more popular in epidemiology. See Souris and Bichaud (2011) for one application and Dixon (2002) for other examples as well as discussion of the difference between the random labelling and the random shifting approaches. Johnson et al. (2007) is an example of a similar permutation approach evaluating near-repeat burglary patterns.

References

  • Baddeley A, Turner R (2005) Spatstat: an R package for analyzing spatial point patterns. J Stat Softw 12(6):1–42

    Article  Google Scholar 

  • Braga AA (2001) The effects of hot spots policing on crime. Annals Am Acad Polit Soc Sci 578(1):104–125

    Article  Google Scholar 

  • Braga AA, Bond BJ (2008) Policing crime and disorder hot spots: a randomized controlled trial. Criminology 46(3):577–607

    Article  Google Scholar 

  • Braga AA, Hureau DM, Papachristos AV (2010a) The relevance of micro places to citywide robbery trends: a longitudinal analysis of robbery incidents at street corners and block faces in Boston. J Res Crime Delinq 48(1):7–32

    Article  Google Scholar 

  • Braga AA, Papachristos AV, Hureau DM (2010b) The concentration and stability of gun violence at micro places in Boston, 1980–2008. J Quant Criminol 26(1):33–53

    Article  Google Scholar 

  • Brantingham PJ, Dyreson DA, Brantingham PL (1976) Crime seen through a cone of resolution. Am Behav Sci 20(2):261–273

    Article  Google Scholar 

  • Caplan JM, Kennedy LW, Miller J (2011) Risk terrain modeling: brokering criminological theory and GIS methods for crime forecasting. JQ 28(2):360–381

    Article  Google Scholar 

  • Cleveland WS, McGill R (1984) Graphical perception: theory, experimentation, and application to the development of graphical methods. J Am Stat Assoc 79(387):531–554

    Article  MathSciNet  Google Scholar 

  • Curman AS, Andresen MA, Brantingham PJ (2014) Crime and place: a longitudinal examination of street segment patterns in Vancouver, BC. J Quant Criminol 31(1):127–147

    Article  Google Scholar 

  • Dixon PM (2002) Ripley’s K function. In: El-Shaarawi AH, Piegorsch WW (eds) Encyclopedia of Environmetrics. Wiley, Chichester, pp 1796–1803

    Google Scholar 

  • Erosheva EA, Matsueda RL, Telesca D (2014) Breaking bad: two decades of life-course data analysis in criminology, developmental psychology, and beyond. Ann Rev Stat App 1(1):301–332

    Article  Google Scholar 

  • Farrell G, Tilley N, Tseloni A (2014) Why the crime drop? Crime Just 43:421–490

    Article  Google Scholar 

  • Genolini C, Falissard B (2010) KmL: k-means for longitudinal data. Comp Stat 25(2):317–328

    Article  MathSciNet  MATH  Google Scholar 

  • Goldstein H (1990) Problem-oriented policing. McGraw-Hill, Inc., New York

    Google Scholar 

  • Groff ER (2014) Quantifying the exposure of street segments to drinking places nearby. J Quant Criminol 30(3):527–548

    Article  Google Scholar 

  • Groff ER, Weisburd D, Yang SM (2010) Is it important to examine crime trends at a local “micro” level?: a longitudinal analysis of street to street variability in crime trajectories. J Quant Criminol 26(1):7–32

    Article  Google Scholar 

  • Hagberg AA, Schult DA, Swart PJ (2008) Exploring network structure, dynamics, and function using NetworkX. In: Varoquauz G, Vaught T, Millmans J (eds) Proceedings of the 7th Python in science conference (SciPy2008) Pasadena, CA

  • Hart T, Zandbergen P (2014) Kernel density estimation and hotspot mapping: examining the influence of interpolation method, grid cell size, and bandwidth on crime forecasting. Polic Int J Police Strateg Manag 37(2):305–323

    Article  Google Scholar 

  • Hinkle JC, Weisburd D, Famega C, Ready J (2013) The problem is not just sample size: the consequences of low base rates in policing experiments in smaller cities. Eval Rev 37(3–4):213–238

    Article  PubMed  Google Scholar 

  • Johnson SD, Bernasco W, Bowers KJ, Elffers H, Ratcliffe JH, Rengert GF, Townsley M (2007) Space–time patterns of risk: a cross national assessment of residential burglary victimization. J Quant Criminol 23(3):201–219

    Article  Google Scholar 

  • Jones BL, Nagin DS (2013) A note on a stata plugin for estimating group-based trajectory models. Soc Methods Res 42(4):608–613

    Article  MathSciNet  Google Scholar 

  • Kreuter F, Muthén B (2008) Analyzing criminal trajectory profiles: bridging multilevel and group based approaches using growth mixture modeling. J Quant Criminol 34(1):1–31

    Article  Google Scholar 

  • Levine N, Kim KE (1998) The location of motor vehicle crashes in Honolulu: a methodology for geocoding intersections. Comput Environ Urban Sysst 22(6):557–576

    Article  Google Scholar 

  • Levine N, Wachs M, Shirazi E (1986) Crime at bus stops: a study of environmental factors. J Archit Plan Res 3(4):339–361

    Google Scholar 

  • Long JS (1997) Regression models for categorical and limited dependent variables. Sage Publications, Thousand Oaks

    MATH  Google Scholar 

  • Lum C, Koper CS, Telep CW (2010) The evidence-based policing matrix. J Exp Criminol 7(1):3–26

    Article  Google Scholar 

  • McDowall D, Loftin C (2009) Do city crime rates follow a national trend? The influence of nationwide conditions on local crime patterns. J Quant Criminol 25(3):307–324

    Article  Google Scholar 

  • Melo SN, Matias LF, Andresen MA (2015) Crime concentrations and similarities in spatial crime patterns in a Brazilian context. Appl Geogr 62:314–324

    Article  Google Scholar 

  • Mohler GO, Short MB, Brantingham PJ, Schoenberg FP, Tita GE (2011) Self-exciting point process modeling of crime. J Am Stat Assoc 106(493):100–108

    Article  MathSciNet  CAS  MATH  Google Scholar 

  • Nagin D, Odgers C (2010) Group-based trajectory modeling (nearly) two decades later. J Quant Criminol 26(4):445–453

    Article  PubMed  PubMed Central  Google Scholar 

  • Nielsen R, Rosenthal JD, Sun Y, Day DM, Bevc I, Duchesne T (2013) Group-based criminal trajectory analysis using the cross-validation criteria. Commun Stat Theory Methods 43(20):4337–4356

    Article  MathSciNet  MATH  Google Scholar 

  • Rey SJ, Mack EA, Koschinsky J (2012) Exploratory space-time analysis of burglary patterns. J Quant Criminol 28(3):509–531

    Article  Google Scholar 

  • Roundtable on Crime Trends in the United States (2015) http://sites.nationalacademies.org/DBASSE/CLAJ/CurrentProjects/DBASSE_081065

  • Shaw CR, McKay HD (1969) Juvenile delinquency and urban areas: a study of rates of delinquency in relation to differential characteristics of local communities in American cities. Revised edition. University of Chicago Press, Chicago

    Google Scholar 

  • Sherman LW, Weisburd D (1995) General deterrent effects of police patrol in crime hot spots: a randomized, controlled trial. Justice Q 12(4):625–648

    Article  Google Scholar 

  • Sherman LW, Gartin PR, Buerger ME (1989) Hot spots of predatory crime: routine activities and the criminology of place. Criminology 27(1):27–55

    Article  Google Scholar 

  • Skardhamar T (2010) Distinguishing facts and artifacts in group-based modeling. Criminology 48(1):295–320

    Article  Google Scholar 

  • Skrondal A, Rabe-Hesketh S (2004) Generalized latent variable modeling: multilevel, longitudinal, and structural equation models. Chapman and Hall/CRC, Boca Rotan

    Book  MATH  Google Scholar 

  • Souris M, Bichaud L (2011) Statistical methods for bivariate spatial analysis in marked points. Examples in spatial epidemiology. Spat Spatio-Temporal Epidemiol 2(4):227–234

    Article  Google Scholar 

  • Weisburd D (2015) The law of crime concentration and the criminology of place. Criminology 53(2):133–157

    Article  Google Scholar 

  • Weisburd D, Amram S (2014) The law of concentrations of crime at place: the case of Tel Aviv-Jaffa. Police Pract Res 15(2):101–114

    Article  Google Scholar 

  • Weisburd D, Gill C (2014) Block randomized trials at places: rethinking the limitations of small n experiments. J Quant Criminol 30(1):97–112

    Article  Google Scholar 

  • Weisburd D, Bushway SD, Lum C, Yang SM (2004) Trajectories of crime at places: a longitudinal study of street segments in the city of Seattle. Criminology 42(2):283–322

    Article  Google Scholar 

  • Weisburd D, Morris NA, Groff ER (2009) Hot spots of juvenile crime: a longitudinal study of arrest incidents at street segments in Seattle, Washington. J Quant Criminol 25(4):443–467

    Article  Google Scholar 

  • Weisburd D, Groff ER, Yang SM (2012) The criminology of place: street segments and our understanding of the crime problem. Oxford University Press, New York

    Book  Google Scholar 

  • Weisburd D, Groff ER, Yang SM (2014) Understanding and controlling hot spots of crime: the importance of formal and informal social controls. Prev Sci 15(1):31–43

    Article  PubMed  Google Scholar 

  • Wilcox P, Eck J (2011) Criminology of the unpopular. Criminol Public Policy 10(2):473–482

    Article  Google Scholar 

  • Yang SM (2010) Assessing the spatial-temporal relationship between disorder and violence. J Quant Criminol 26(1):139–163

    Article  CAS  Google Scholar 

Download references

Acknowledgments

This research was supported by Award No. 2013-IJ-MU-0012, awarded by the National Institute of Justice, Office of Justice Programs, U.S. Department of Justice, to the John F. Finn Institute. The opinions, findings, and conclusions or recommendations in this article are those of the authors and do not necessarily reflect those of the Department of Justice.

Author information

Authors and Affiliations

  1. The John F. Finn Institute for Public Safety, Inc., 421 New Karner Rd. Suite 12, Albany, NY, 12205, USA

    Andrew P. Wheeler, Robert E. Worden & Sarah J. McLean

  2. University at Albany, SUNY, Albany, NY, USA

    Andrew P. Wheeler & Robert E. Worden

Authors
  1. Andrew P. Wheeler
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robert E. Worden
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sarah J. McLean
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andrew P. Wheeler.

Appendices

Appendix 1: Crosstabs of Clustering Solutions for Different Crime Subsets

This appendix contains cross-tabulations for separate group based trajectory modelling solutions for all penal law crimes (what is presented in the paper) versus group based trajectory models for only subsets of Part 1 and Part 2 UCR crimes. Part 1 crimes include homicide, rape, robbery, aggravated assault, burglary, larceny, theft of a motor vehicle, and arson. Part 2 crimes are all other penal law crimes not listed as Part 1 crimes. These crimes include all reported offenses between 2000 and 2013, and each incident is classified according to the most serious charge (according to the UCR hierarchy).

Equivalent group-based trajectory models were estimated for these subsets of data, using the same parameters and model based selection criteria as that presented in the paper. For Part 1 crimes the seven group solution was chosen, and for Part 2 crimes the six group solution was chosen. Trajectory groups labeled with lower numbers have higher mean level trends (same as the models presented in the paper).

Tables 5, 6 and 7 show that the estimated trajectory groups based on the different subsets have strong overlap. Visualization of the trajectories (not shown) also shows that the different crime subsets behave quite similarly to the overall crime trajectories: most of the groups are simply separated by the mean level of crime. Tables 5, 6 and 7 display contingency tables showing the overlap of each of these trajectory solutions. Table 5 displays the overlap of group-based solutions for Part 1 and Part 2 crimes, Table 6 displays the overlap for Part 1 crimes and all crimes, and Table 7 displays the overlap between Part 2 crimes and all crimes.

Table 5 Part 2 and part 1 crime group trajectories
Full size table
Table 6 Part 1 and all crime group trajectories
Full size table
Table 7 Part 2 and all crime group trajectories
Full size table

Appendix 2: Overview Map of Albany

Figure 8 presents an overview map of the city of Albany. Land use parcels are symbolized as either light grey (commercial or mixed properties) or residential land uses are colored as light blue. Parks are superimposed on the parcels as green areas, and the foremost geographic layer is the street network. In the street network highways are symbolized with darker outlines and light grey middle areas, whereas other streets are given a solid color. Main arterial streets are drawn in a darker color and slightly thicker than side streets. Finally, approximate neighborhood locations are labelled on the map.

Fig. 8
figure 8

Overview map of Albany displaying land use patterns and streets. Approximate neighborhood locations are labelled

Full size image

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wheeler, A.P., Worden, R.E. & McLean, S.J. Replicating Group-Based Trajectory Models of Crime at Micro-Places in Albany, NY. J Quant Criminol 32, 589–612 (2016). https://doi.org/10.1007/s10940-015-9268-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10940-015-9268-3

Keywords

Search

Navigation