Skip to main content

Is it Important to Examine Crime Trends at a Local “Micro” Level?: A Longitudinal Analysis of Street to Street Variability in Crime Trajectories

Abstract

Over the last 40 years, the question of how crime varies across places has gotten greater attention. At the same time, as data and computing power have increased, the definition of a ‘place’ has shifted farther down the geographic cone of resolution. This has led many researchers to consider places as small as single addresses, group of addresses, face blocks or street blocks. Both cross-sectional and longitudinal studies of the spatial distribution of crime have consistently found crime is strongly concentrated at a small group of ‘micro’ places. Recent longitudinal studies have also revealed crime concentration across micro places is relatively stable over time. A major question that has not been answered in prior research is the degree of block to block variability at this local ‘micro’ level for all crime. To answer this question, we examine both temporal and spatial variation in crime across street blocks in the city of Seattle Washington. This is accomplished by applying trajectory analysis to establish groups of places that follow similar crime trajectories over 16 years. Then, using quantitative spatial statistics, we establish whether streets having the same temporal trajectory are collocated spatially or whether there is street to street variation in the temporal patterns of crime. In a surprising number of cases we find that individual street segments have trajectories which are unrelated to their immediately adjacent streets. This finding of heterogeneity suggests it may be particularly important to examine crime trends at very local geographic levels. At a policy level, our research reinforces the importance of initiatives like ‘hot spots policing’ which address specific streets within relatively small areas.

This is a preview of subscription content, access via your institution.

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

Notes

  1. Due to space constraints only selected references are mentioned here. More complete overviews of the history of place-based criminology can be found in the introductory chapters of Eck and Weisburd (1995) and Weisburd et al. (2008).

  2. For an exception see Groff et al. 2008. They use the same methodology but explore the patterns of crimes committed by juveniles.

  3. The literature around hot spots is immense. Two recent overviews provide the insight into the state of the art (Chainey et al. 2008; Eck et al.2005). See Weisburd et al. (1992) for a theoretical introduction.

  4. Weisburd et al. (2004a, b) came at this from the opposite direction. They first identified temporal trends in crime and then used kernel density maps to find hotspots of temporal trajectory patterns.

  5. The volume of research explicitly examining spatial dependence or spatial error in models is far too large to detail here (as examples see Baller et al. 2001; Chakravorty and Pelfrey 2000; Cohen and Tita 1999; Cork 1999; Jefferis 2004; Morenoff and Sampson 1997; Roman 2002).

  6. This unit of analysis is slightly different from the ‘hundred block’ measure used in the original Seattle study. See the final report for more information on the ‘hundred block’ definition (Weisburd et al. 2004b). More detailed information on the creation of geographically defined street segment is available (see Weisburd et al. 2009a).

  7. There are two main reasons for excluding intersection crime. First, since events at intersections could be considered ‘part of’ any one of the participating street segments, there is no satisfactory method for assigning them to one or another. However, it is also the case that incident reports at intersections differed dramatically from those at street segments. Traffic-related incidents accounted for only 3.77% of reports at street segments, but for 45.3% of reports at intersections.

  8. All geocoding was done in ArcGIS 9.1 using a geocoding locator service with an alias file of common place names to improve our hit rate. The geocoding locater used the following parameters: spelling sensitivity = 80, minimum candidate score = 30, minimum match score = 85, side offset = 0, end offset 3%, and Match if candidates tie = no. Manual geocoding was done on unmatched records in ArcGIS 9.1 and then in ArcView 3.x using the ‘MatchAddressToPoint’ tool (which allowed the operator to click on the map to indicate where an address was located) to improve the overall match rate. Research has suggested hit rates above 85% are reliable (Ratcliffe 2004). Our final geocoding percentage for crime incidents was 97.3%.

  9. In order to apply point pattern statistics to street segments we use the midpoint of each line/street to represent the street segment.

  10. This is accomplished by using a series of random toroidal shifts on one set of points and comparing the cross K-function of the shifted points with another fixed set (Rowlingson and Diggle 1993). A toroidal shift provides a simulation of potential outcomes under the assumption of independence by repeatedly and randomly shifting the set of locations for one type of street segment and calculating the cross K-function for that iteration. The outcomes are used to create test statistics in the form of an upper and lower envelope. One thousand iterations are used for each simulation. In order to better explore micro level relationships, the bivariate - K analysis examines the distribution of the trajectory pairs at distances up to 2,800 feet (using 400 foot bins which approximate one street block). This strategy also allows us to more closely inspect the relationship of the bivariate k statistic to the upper bound of the simulation envelope. The null hypothesis of the bivariate- K test is independence (i.e., the spatial pattern of one trajectory group is unrelated to the pattern of the other group being compared).

  11. Readers should note slight scale changes among maps 1, 2 and 3. These were necessary to provide maximum enlargement of the three sections of Seattle.

  12. Ripley’s K also reveals whether the observed clustering is greater or less than would be expected under an assumption of Complete Spatial Randomness (CSR). CSR is of limited use when examining human-related distributions such as crime because the opportunity for a crime to occur is constrained to accessible areas adjacent to streets. By calculating the Ripley’s K for the street network, we can provide a more realistic metric with which to compare patterns in the trajectory group member ship of street segments (see ‘Street segments’ line in Fig. 4).

  13. These analyses produced 28 graphs. Space constraints do not allow the inclusion of the graphs in the paper; however, they are available from the authors.

  14. The group-based trajectory is often identified with typological theories of offending such as Moffitt (1993) because of its use of groups (see Nagin et al. 1995). But it is important to keep in mind that group assignments are made with error. In all likelihood, the groups only approximate a continuous distribution. The lack of homogeneity in the groups is the explicit trade off for the relaxation of the parametric assumptions about the random effects in the linear models (Bushway et al. 2003). For a different perspective on this issue, see Eggleston et al. (2004).

  15. Those interested in a more detailed description of the group-based trajectory approach should see Nagin (1999) or (2005).

  16. The procedure, with documentation, is available at www.ncovr.heinz.cmu.edu.

  17. Proc Traj also provides the option of estimating a Zero Inflated Poisson (ZIP) model. The ZIP model builds on a Poisson by accommodating more non-offenders in any given period than predicted by the standard Poisson distribution. The zero-inflation parameter can be allowed to vary over time, but cannot be estimated separately for each group. It is sometimes called an intermittency parameter, since it allows places to have “temporary” spells of no offenses without recording a change in their overall rate of offending. In this context, the ZIP model’s differentiation between short-term and long-term change is problematic. The Poisson model, on the other hand, tracks movement in the rate of offending in one parameter, allowing all relatively long-term changes to be reflected in one place. We believe this trait of the Poisson model makes it the better model for modeling trends, especially over relatively short panels, even though the ZIP model provides a better fit according to the BIC criteria used for model selection. For a similar argument see Bushway et al. (2003).

References

  • Aitken SC, Cutter SL, Foote KE, Sell JL (1989) Environmental perception and behavioral geography. In: Wilmott Gaile (ed) Geography in America. Columbus, Merrill, pp 218–238

    Google Scholar 

  • Bailey TC, Gatrell AC (1995) Interactive spatial data analysis. Longman Group Limited, Essex

    Google Scholar 

  • Baller RD, Anselin L, Messner Steven F, Deane G, Hawkins DF (2001) Structural covariates of US county homicide rates: incorporating spatial effects. Criminology 39:561–590

    Article  Google Scholar 

  • Baumer EP, Lauritsen JL, Rosenfeld R, Wright R (1998) The influence of crack cocaine on robbery, burglary, and homicide rates: a cross-city, longitudinal analysis. J Res Crime Delinq 35:316–340

    Article  Google Scholar 

  • Boggs S (1965) Urban crime patterns. Am Sociol Rev 30:899–908

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Braga AA, Papachristos AV, Hureau D (2009) The concentration and stability of gun violence at micro places in Boston, 1980–2008. J Quant Criminol. doi:10.1007/s10940-009-9082-x

  • Brantingham PJ, Brantingham PL (1984) Patterns in crime. Macmillan, New York

    Google Scholar 

  • Brantingham PJ, Brantingham PL (1991) Environmental criminology. Waveland Press, Inc., Prospect Heights (1981)

    Google Scholar 

  • Brantingham PL, Brantingham PJ (1993) Environment, routine, and situation: toward a pattern theory of crime. In: Clarke RV, Felson M (eds) Routine activity and rational choice, vol 5. Transaction Publishers, New Brunswick, pp 259–294

    Google Scholar 

  • Brantingham PL, Brantingham PJ (1995) Criminality of place: crime generators and crime attractors. Eur J Crim Pol Res 3:5–26

    Article  Google Scholar 

  • Brantingham PL, Brantingham PJ (1999) Theoretical model of crime hot spot generation. Stud Crime Crime Prev 8:7–26

    Google Scholar 

  • Brantingham PL, Brantingham PJ (2008) Crime analysis at multiple scales of aggregation: a topological approach. In: Weisburd D, Bernasco W, Bruinsma G (eds) Putting crime in its place: units of analysis in spatial crime research. Springer, New York, pp 87–108

    Google Scholar 

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

    Article  Google Scholar 

  • Bursik RJJ, Grasmick HG (1993) Neighborhoods and crime: the dimensions of effective community control. Lexington Books, New York

    Google Scholar 

  • Bursik RJJ, Webb J (1982) Community change and patterns of delinquency. Am J Soc 88:24–42

    Article  Google Scholar 

  • Bushway SD, Thornberry TP, Krohn MD (2003) Desistance as a developmental process: a comparison of static and dynamic approaches. J Quant Criminol 19:129–153

    Article  Google Scholar 

  • Byrne JM, Sampson RJ (eds) (1986) Social ecology of crime. Springer, New York

    Google Scholar 

  • Chainey S, Tompson L, Uhlig S (2008) The utility of hotspot mapping for predicting spatial patterns of crime. Secur J 21:4–28

    Article  Google Scholar 

  • Chakravorty S, Pelfrey WVJ (2000) Exploratory data analysis of crime patterns: preliminary findings from the Bronx. In: Goldsmith V, McGuire P, Mollenkopf G,JH, Ross TA (eds) Analyzing crime patterns: frontiers of practice. Sage Publications, Thousand Oaks, pp 65–76

    Google Scholar 

  • Chilton RJ (1964) Continuity in delinquency area research: a comparison of studies for Baltimore, Detroit, and Indianapolis. Am Sociology Rev 29:71–83

    Article  Google Scholar 

  • Clarke RV (1983) Situational crime prevention: its theoretical basis and practical scope. In: Tonry M, Morris N (eds) Crime and justice: an annual review of research, vol 14. University of Chicago Press, Chicago, pp 225–256

    Google Scholar 

  • Clarke RV, Felson M (1993) Introduction: criminology, routine activity, and rational choice. In: Clarke RV, Felson M (eds) Routine activity and rational choice, vol 5. Transaction Publishers, New Brunswick, pp 1–14

    Google Scholar 

  • Cohen LE, Felson M (1979) Social change and crime rate trends: a routine activity approach. Am Sociol Rev 44:588–608

    Article  Google Scholar 

  • Cohen J, Tita G (1999) Diffusion in homicide: exploring a general method for detecting spatial diffusion processes. J Quant Criminol 15:451–493

    Article  Google Scholar 

  • Cork D (1999) Examining space-time interaction in city-level homicide data: crack markets and the diffusion of guns among youth. J Quant Criminol 15:379–406

    Article  Google Scholar 

  • Crow W, Bull J (1975) Robbery deterrence: an applied behavioral science demonstration—final report. Western Behavioral Science Institute, La Jolla

    Google Scholar 

  • D’Unger AV, Land KC, McCall PL, Nagin DS (1998) How many latent classes of delinquent/criminal careers? Results form mixed poisson regression analysis. Am J Sociol 103:1593–1630

    Article  Google Scholar 

  • Eck JE (1995) Examining routine activity theory: a review of two books. JQ 12:783–797

    Article  Google Scholar 

  • Eck JE, Weisburd D (1995) Crime places in crime theory. In: Eck JE, Weisburd D (eds) Crime and place. Willow Tree Press, Monsey, NY, pp 1–33

    Google Scholar 

  • Eck JE, Chainey S, Cameron JG, Leitner M, Wilson RE (2005) Mapping crime: understanding hotspots. National Institute of Justice, Washington, DC

    Google Scholar 

  • Eggleston EP, Laub JH, Sampson RJ (2004) Methodological sensitivities to latent class analysis of longterm criminal trajectories. J Quant Criminol 20:1–26

    Article  Google Scholar 

  • Felson M (1986) Predicting crime potential at any point on the city map. In: Figlio RM, Hakim S, Rengert GF (eds) Metropolitan crime patterns. Criminal Justice Press, Monsey, pp 127–136

    Google Scholar 

  • Felson M (1987) Routine activities and crime prevention in the developing metropolis. Criminology 25:911–931

    Article  Google Scholar 

  • Felson M (2002) Crime in everyday life, 3rd edn. Sage, Thousand Oaks

    Google Scholar 

  • Fotheringham AS, Brundson C, Charlton M (2000) Quantitative geography. Sage Publications, London

    Google Scholar 

  • Gold JR (1980) An introduction to behavioural geography. Oxford University Press, New York

    Google Scholar 

  • Golledge RG, Timmermans H (1990) Applications of behavioural research on spatial problems I: cognition. Prog Hum Geogr 14:57–99

    Article  Google Scholar 

  • Griffiths E, Chavez JM (2004) Communities, street guns, and homicide trajectories in Chicago, 1980–1995: merging methods for examining homicide trends across space and time. Criminology 42:941–978

    Article  Google Scholar 

  • Groff ER, LaVigne NG (2001) Mapping an opportunity surface of residential burglary. J Res Crime Delinq 38:257–278

    Article  Google Scholar 

  • Groff ER, Weisburd D, Morris N (2008) Where the action is at places: examining spatio-temporal patterns of juvenile crime at places using trajectory analysis and GIS. In: Weisburd D, Bernasco W, Bruinsma G (eds) Putting crime in its place: units of analysis in spatial crime research. Springer, Berlin

    Google Scholar 

  • Grubesic TH, Mack EA (2008) Spatio-temporal interaction of urban crime. J Quant Criminol 24:285–306

    Article  Google Scholar 

  • Guerry A-M (1833) Essai sur la Statisticque morale de la France. Crochard, Paris

    Google Scholar 

  • Hillier B (1999) The common language of space: a way of looking at the social, economic and environmental functioning of cities on a common basis. Retrieved February 17, 2004, from http://www.spacesyntax.org/publications/commonlang.html

  • Hillier B (2004) Can streets be made safe? Urban Des Int 9:31–45

    Article  Google Scholar 

  • Jacobs J (1961) The death and life of great American cities. Vintage Books, New York

    Google Scholar 

  • Jefferis E (2004) Criminal places: a micro-level study of residential theft . Unpublished Dissertation, University of Cincinnati, Cincinnati

  • Jeffery CR (1971) Crime prevention through environmental design. Sage Publications, Beverly Hills

    Google Scholar 

  • Johnson SD, Lab SP, Bowers KJ (2008) Stable and fluid hotspots of crime: differentiation and identification. Built Environ 34:32–45

    Article  Google Scholar 

  • Jones BL, Nagin DS, Roeder K (2001) A SAS procedure based on mixture models for estimating developmental trajectories. Sociol Methods Res 29:374–393

    Article  Google Scholar 

  • Kaluzney SP, Vega SC, Cardoso TP, Shelly AA (1998) S+SpatialStats: users manual for Windows and UNIX. Insightful, Seattle, WA

    Google Scholar 

  • Kinney JB, Brantingham PL, Wuschke K, Kirk MG, Brantingham PJ (2009) Crime attractors, generators and detractors: land use and urban crime opportunities. Built Environ 34:62–74

    Article  Google Scholar 

  • Kornhouser R (1978) Social sources of delinquency: an appraisal of analytic models. University of Chicago, Chicago

    Google Scholar 

  • Kubrin CE, Herting JR (2003) Neighborhood correlates of homicide trends: an analysis using growth-curve modeling. Sociol Quart 44:329–350

    Article  Google Scholar 

  • Lab SP (2007) Crime prevention: approaches, practices, evaluations. Anderson Publishing, Cincinnati

    Google Scholar 

  • Lehoczky J (1986) Random parameter stochastic process models of criminal careers. In: Blumstein A, Cohen J, Roth JA, Visher CA (eds) Criminal careers and career criminals. National Academy of Sciences Press, Washington, DC

    Google Scholar 

  • Levine N (2005) CrimeStat: a spatial statistics program for the analysis of crime incident locations, vol 3.0. Ned Levine & Associates, Houston, TX and National Institute of Justice, Washington, DC

  • Linnell D (1988) The geographic distribution of hot spots of robbery, rape, and auto theft in Minneapolis . Unpublished MA, University of Maryland, College Park

  • Loftin C, Hill RH (1974) Regional subculture and homicide: an examination of the Gastil-Hackney thesis. Am Sociol Rev 39:714–724

    Google Scholar 

  • Maltz MD (1996) From Poisson to the present: applying operations research to problems of crime and justice. J Quant Criminol 12(1):3–61

    Article  Google Scholar 

  • Merry SE (1981) Defensible space undefended: social factors in crime control through environmental design. Urban Aff Q 16:397–422

    Article  Google Scholar 

  • Messner SF, Anselin L (2004) Spatial analysis of homicide with areal data. In: Goodchild MF, Janelle DG (eds) Spatially integrated social science. Oxford University Press, New York, pp 127–144

    Google Scholar 

  • Moffitt TE (1993) Adolescence-limited and life-course persistent antisocial behavior: a developmental taxonomy. Psychol Rev 100:674–701

    Article  Google Scholar 

  • Morenoff JD, Sampson RJ (1997) Violent crime and the spatial dynamics of neighborhood transition: Chicago, 1970–1990. Soc Forces 76:31–64

    Article  Google Scholar 

  • Nagin DS (1999) Analyzing developmental trajectories: a semiparametric group-based approach. Psychol Methods 4:139–157

    Article  Google Scholar 

  • Nagin DS (2005) Group-based modeling of development over the life course. Harvard University Press, Cambridge

    Google Scholar 

  • Nagin DS, Land KC (1993) Age, criminal careers, and population heterogeneity: specification and estimation of a nonparametric, mixed poisson model. Criminology 31:327–362

    Article  Google Scholar 

  • Nagin DS, Farrington DP, Moffitt TE (1995) Life-course trajectories of different types of offenders. Criminology 33:111–139

    Article  Google Scholar 

  • Newman O (1972) Defensible space: crime prevention through environmental design. Macmillan, New York

    Google Scholar 

  • Oberwittler D, Wikstrom P-O (2008) Why small is better: advancing the study of the role of behavioral context in crime causation. In: Weisburd D, Bernasco W, Bruinsma G (eds) Putting crime in its place: units of analysis in spatial crime research, vol 35–60. Springer, New York

    Google Scholar 

  • Osgood DW (2000) Poisson-based regression analysis of aggregate crime rates. J Quant Criminol 16(1):21–43

    Article  Google Scholar 

  • Pierce G, Spaar S, Briggs LR (1986) The character of police work: strategic and tactical implications. Center for Applied Social Research, Northeastern University, Boston

    Google Scholar 

  • Potchak MC, McGloin JM, Zgoba KM (2002) A spatial analysis of criminal effort: auto theft in Newark, New Jersey. Crim Just Pol Rev 13:257–285

    Article  Google Scholar 

  • Quetelet AJ (1831[1984]) Research on the propensity for crime at different ages (trans: Test Sylvester SF). Anderson Publishing Co, Cincinnati

  • Ratcliffe JH (2004) Geocoding crime and a first estimate of a minimum acceptable hit rate. Int J Geogr Inf Syst 18:61–72

    Article  Google Scholar 

  • Raudenbush SW (2001) Comparing personal trajectories and drawing causal inferences from longitudinal data. Annu Rev Psychol 52:501–525

    Google Scholar 

  • Reiss A J Jr, Tonry M (1986) Preface. In: Reiss A J Jr, Tonry M (eds) Communities and crime. University of Chicago Press, Chicago, pp 1–34

    Google Scholar 

  • Rengert G, Lockwood B (2008) Geographical units of analysis and the analysis of crime. In: Weisburd D, Bernasco W, Bruinsma G (eds) Putting crime in its place: units of analysis in spatial crime research, vol 109–122. Springer, New York

    Google Scholar 

  • Robinson JB, Lawton BA, Taylor RB, Perkins DD (2003) Multilevel longitudinal impacts of incivilities: fear of crime, expected safety, and block satisfaction. J Quant Criminol 19:237–274

    Article  Google Scholar 

  • Roman CG (2002) Schools as generators of crime: routine activities and the sociology of place . Unpublished Dissertation, American University, Washington DC

  • Roncek DW (2000) Schools and crime. In: Goldsmith V, McGuire P, Mollenkopf G,JH, Ross TA (eds) Analyzing crime patterns: frontiers of practice. Sage Publications, Thousand Oaks, pp 153–165

    Google Scholar 

  • Rowlingson BS, Diggle PJ (1993) Splancs: spatial point pattern analysis code in S-plus. Comput Geosci 19:627–655

    Article  Google Scholar 

  • Sampson RJ, Raudenbush SW (1999) Systematic social observation of public spaces: a new look at disorder in urban neighborhood s. Am J Soc 105:603–651

    Article  Google Scholar 

  • Schuerman L, Kobrin S (1986) Community careers in crime. In: Reiss AJJ, Tonry M (eds) Communities and crime. University of Chicago, Chicago, pp 67–100

    Google Scholar 

  • Sherman LW (1995) Hot spots of crime and criminal careers of places. In: Eck J, Weisburd DL (eds) Crime and place, vol 4. Willow Tree Press, Monsey

    Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Skogan WG (1986) Fear of crime and neighborood change. In: Reiss AJJ, Tonry M (eds) Communities and crime. University of Chicago Press, Chicago, pp 203–230

    Google Scholar 

  • Smith WR, Frazee SG, Davison EL (2000) Furthering the integration of routine activity and social disorganization theories: small units of analysis and the study of street robbery as a diffusion process. Criminology 38:489–523

    Article  Google Scholar 

  • Spring JV, Block CR (1988) Finding crime hot spots: experiments in the identification of high crime areas. Paper presented at the Midwest Sociological Society

  • Stark R (1987) Deviant places: a theory of the ecology of crime. Criminology 25:893–909

    Article  Google Scholar 

  • Taylor RB (1997) Social order and disorder of street blocks and neighborhoods: ecology, microecology, and the systemic model of social disorganization. J Res Crime Delinq 34:113–155

    Article  Google Scholar 

  • Taylor RB (1998) Crime and small-scale places: what we know, what we can prevent, and what else we need to know. In: Taylor RB, Bazemore G, Boland B, Clear TR, Corbett RPJ, Feinblatt J, Berman G, Sviridoff M, Stone C (eds) Crime and place: plenary papers of the 1997 conference on criminal justice research and evaluation, National Institute of Justice, Washington, DC, pp 1–22

  • Taylor RB (2001) Breaking away from broken Windows: baltimore neighborhoods and the nationwide fight against crime, grime, fear and decline. Westview Press, Boulder

    Google Scholar 

  • Taylor RB, Gottfredson SD (1986) Enivronmental design, crime, and prevention: an examination of community dynamics. In: Reiss A J Jr, Tonry M (eds) Communities and crime. University of Chicago Press, Chicago, pp 387–416

    Google Scholar 

  • Taylor RB, National Consortium on Violence Research (1999) A longitudinal look at the incivilities thesis: does disorder bring later crime and decline? Paper presented at the Eastern Sociological Association, Boston, MA

  • Timmermans H, Golledge RG (1990) Applications of behavioural research on spatial problems II: preference and choice. Prog Hum Geogr 14:311–354

    Article  Google Scholar 

  • van Wilselm J (2008) Urban streets as micro contexts to commit violence. In: Weisburd D, Bernasco W, Bruinsma G (eds) Putting crime in its place: units of analysis in spatial crime research. Springer, Berlin, pp 199–216

    Google Scholar 

  • Walmsley DJ, Lewis GJ (1993) People and environment: behavioral approaches in human geography. Longman Scientific & Technical, Essex

    Google Scholar 

  • Weisburd D (2002) From criminals to criminal contexts: reorienting crime prevention. In: Waring E, Weisburd D (eds) Crime & social organization, vol 10. Transactions Publishers, New Brunswick, pp 197–216

    Google Scholar 

  • Weisburd D, Braga AA (2002) Hot spots policing. In: Kury H, Fuchs O (eds) Crime prevention: new approaches. Mainz, Germany, Weisner Ring

    Google Scholar 

  • Weisburd D, Green L (1994) Defining the drug market: the case of the Jersey City DMA system. In: MacKenzie DL, Uchida CD (eds) Drugs and crime: evaluating public policy initiatives. Sage, Newbury Park

    Google Scholar 

  • Weisburd D, Green L (1995) Policing drug hot spots: the Jersey City drug market analysis experiment. JQ 12:711–735

    Article  Google Scholar 

  • Weisburd D, Mazerolle L (2000) Drug hot spots and crime. Police Quart 3:331–349

    Article  Google Scholar 

  • Weisburd D, McEwen T (1997) Introduction: crime mapping and crime prevention. In: Weisburd DL, McEwen T (eds) Crime mapping and crime prevention: crime prevention studies, vol 8. Criminal Justice Press, Monsey, pp 1–26

    Google Scholar 

  • Weisburd D, Maher L, Sherman LW (1992) Contrasting crime general and crime specific theory: the case of hot spots of crime. In: Adler F, Laufer WS (eds) Advances in criminological theory, vol 4. Transaction Press, New Brunswick, NJ, pp 45–70

    Google Scholar 

  • Weisburd D, Bushway S, Lum C, Yang S-M (2004a) Trajectories of crime at places: a longitudinal study of street segments in the city of Seattle. Criminology 42:283–321

    Article  Google Scholar 

  • Weisburd D, Lum C, Yang S-M (2004b) The criminal careers of places: a longitudinal study. US Department of Justice, National Institute of Justice, Washington, DC

    Google Scholar 

  • Weisburd D, Bruinsma G, Bernasco W (2008) Units of analysis in geographic criminology: historical development, critical issues and open questions. In: Weisburd D, Bernasco W, Bruinsma G (eds) Putting crime in its place: units of analysis in spatial crime research. Springer, New York, pp 3–31

    Google Scholar 

  • Weisburd D, Groff E, Yang S-M (2009a) Explaining developmental crime trajectories at places: a study of “crime waves” and “crime drops” at micro units of geography. National Institute of Justice, Washington DC (in progress)

  • Weisburd D, Morris N, Groff ER (2009b) Hot spots of juvenile crime: a longitudinal study of street segments in Seattle, Washington. J Quant Criminol 24:443–467

    Article  Google Scholar 

  • Weisburd D, Groff E, Yang S-M (under review) Understanding developmental crime trajectories at places: social disorganization and opportunity perspectives at micro units of geography. National Institute of Justice, Washington, DC

  • Wolfgang ME, Figlio RM, Sellin T (1972) Delinquency in a birth cohort. The University of Chicago Press, Chicago

    Google Scholar 

Download references

Acknowledgments

This research was supported by grant 2005-IJ-CX-0006 from the National Institute of Justice (US Department of Justice). Points of view in this paper are those of the authors and do not necessarily represent those of the US Department of Justice. We would like to thank Dan Nagin for his thoughtful suggestions regarding trajectory analysis, Richard Heiberger for his assistance with R programming, and Breanne Cave and the anonymous reviewers whose comments were invaluable in strengthening the paper. We also want to express our gratitude for the cooperation of the Seattle Police Department, and especially to Lieutenant Ron Rasmussen for playing the crucial role of our main data contact and former Chief Gil Kerlikowske (now Director of the Office of National Drug Control Policy) for his interest in and support of our work.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Elizabeth R. Groff.

Appendix 1: Technical Note of the Production of Developmental Trajectories for Street Segments

Appendix 1: Technical Note of the Production of Developmental Trajectories for Street Segments

The trajectory modeling reported here was developed for a larger study of crime and place in Seattle, WA (Weisburd et al. 2009a). The group-based trajectory model, first described by Nagin and Land (1993) and further elaborated in Nagin (1999, 2005), is specifically designed to identify clusters of individuals with similar developmental trajectories, and it has been utilized extensively to study patterns of change in offending and aggression as people age (see Nagin 1999). As such, we believe it is particularly well suited to our goal of exploring the patterns of change in the Seattle data.

Formally, the model specifies that the population is comprised of a finite number of groups of individuals who follow distinctive developmental trajectories. Each such group is allowed to have its own offending trajectory (a map of offending rates throughout the time period) described by a distinct set of parameters that are permitted to vary freely across groups. This type of model has three key outputs: the parameters describing the trajectory for each group, the estimated proportion of the population belonging to each group, and the posterior probability of belonging to a given group for each individual in the sample. The posterior probability, which is the probability of group membership after the model is estimated, can be used to assign individuals to a group based on their highest probability.Footnote 14

This approach is less efficient than linear growth models but allows for qualitatively different patterns of behavior over time. There is broad agreement that delinquency and crime are cases where this group-based trajectory approach might be justified, in large part because not everyone participates in crime, and people appear to start and stop at very different ages (Nagin 1999, 2005; Raudenbush 2001). Given that we have no strong expectation about the basic pattern of change, the group-based trajectory approach appears to be an excellent choice for identifying major patterns of change in our data set.Footnote 15

There are two software packages available that can estimate group-based trajectories: Mplus, a proprietary software package, and Proc Traj, a special procedure for use in SAS, made available at no cost by the National Consortium on Violence Research (for a detailed discussion of Proc Traj, see Jones et al. 2001).Footnote 16 In using Proc Traj, we had three choices when estimating trajectories of count data: parametric form (Poisson vs. normal vs. logit), functional form of the trajectory over time (linear vs. quadratic vs. cubic), and number of groups.

The Poisson distribution is a standard distribution used to estimate the frequency distribution of offending that we would expect given a certain unobserved offending rate (Lehoczky 1986; Maltz 1996; Osgood 2000).Footnote 17 We found that the quadratic was uniformly a better fit than the linear model, and that the cubic model did not improve the fit over the quadratic in the case of a small number of groups. In choosing the number of groups we relied upon the Bayesian Information Criteria (BIC) because conventional likelihood ratio tests are not appropriate for defining whether the addition of a group improves the explanatory power of the model (D’Unger et al. 1998). BIC = log( L) − .5 × log( n) × ( k); where “ L” is the value of the model’s maximized likelihood estimates, “ n” is the sample size, and “ k” is the number of parameters estimated in a given model. Because more sophisticated models almost always improve the fit of a given analysis, the BIC encourages a parsimonious solution by penalizing models that increase the number of trajectories unless they substantially improve fit. In addition to the BIC, trajectory analysis requires that researchers also consider posterior probabilities of trajectory assignments, odds of correct classification, estimated group probabilities, and whether meaningful groups are revealed (for a more detailed discussion, see Nagin 2005).

These models are highly complex, and researchers run the risk of arriving at a local maximum, or peak in the likelihood function, which represents a sub-optimal solution. The stability of the answer when providing multiple sets of starting values should be considered in any model choice. In the final analysis, the utility of the groups is determined by their ability to identify distinct trajectories, the number of units in each group, and their relative homogeneity (Nagin 2005).

We began our modeling exercise by fitting the data to three trajectories. We then fit the data to four trajectories and compared this fit with the three-group solution. When the four-group model proved better than the three-group, we then estimated the five-group model and compared it to the four-group solution. We continued adding groups, each time finding an improved BIC, until we arrived at 24 groups. Models for 23 and 24 groups were not stable and could not be replicated consistently. After reviewing the Bayesian Information Criteria and the patterns observed in each solution, it was determined that a 22 group model was the most optimal model for the crime data. We therefore chose the 22 group model.

The validity of the model was also confirmed by conducting the posterior probability analysis. The majorities of the within-group posterior probabilities in the model are above .90, and the lowest posterior probability is .77. The lowest value of the odds of correction classification (OCC) is 26.58. Nagin (2005) suggests that when average posterior probability is higher than .7 and OCC values are higher than 5, the group assignment represents a high level of accuracy. Judging by these standards, the 22-group model performs satisfactorily in classifying the various crime patterns into separate trajectories.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Groff, E.R., Weisburd, D. & Yang, SM. 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, 7–32 (2010). https://doi.org/10.1007/s10940-009-9081-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10940-009-9081-y

Keywords

  • Crime concentration
  • Hot spots
  • Micro
  • Spatio-temporal