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



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.


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.


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.


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.

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  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,

  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.


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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.

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Correspondence to Andrew P. Wheeler.


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
Table 6 Part 1 and all crime group trajectories
Table 7 Part 2 and all crime group trajectories

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

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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).

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  • Group-based trajectory
  • Micro-places
  • Hot-spots
  • Point-pattern
  • Spatial criminology