How Exactly Does Place Matter in Crime Analysis? Place, Space, and Spatial Heterogeneity

Abstract

This article has four aims. First is to clarify the origins and different meanings of place, space, and other basic concepts in spatial analysis. The second aim is to reiterate the illogicality of the spatial homogeneity assumption in ordinary least squares (OLS) regression. An illustration of the comparison between traditional OLS and geographically weighted regression modeling is included for this purpose. The third aim is to explain that place matters in crime analysis not only when crime data are spatially clustered, but when relationships between correlates are found to be conditional upon place. The final aim is to convince criminology and criminal justice faculty to begin discussing the inclusion of spatial modeling as a compulsory topic in the curriculum.

Acknowledgements

I want to thank Professor Ahmed El-Geneidy and his team of graduate research students at McGill University for their warm welcoming to their spatial analysis lab. In particular I must thank Devon Willis (BA, McGill) for her proof-reading of the manuscript. I must also thank two reviewers, whose suggestions and comments resulted, I hope, in a much better article. Clearly, all errors are mine alone.

Notes

1. See Vilalta (2005).

2. This is a mathematical definition of location. There are other definitions of location as a site or toponym.

3. Habraken (1998) makes this statement in reference to social processes.

4. Metropolitan areas in their case.

5. For instance, cities and neighborhoods illustrate the long-lasting effects of the ideologies, technologies, design trends, cultural tastes, and even moods of their residents over time.

6. Classical Greek had no word for space (Elden, 2010). Interestingly enough, ambitus was also the term given to a crime of political corruption, basically vote buying and vote coercion, in ancient Rome.

7. And in other disciplines in the social sciences.

8. When depth is incorporated in polygons we enter the third dimension of things.

9. In Euclidean geometry, space can only be seen in three dimensions.

10. Rose (1936, p. 90) was probably the first geographer “… to illustrate the possibilities of what may well be called statistical method in geography” by using linear correlation analysis. However, it seems that it was Fisher the first to warn about the issue of spatial dependence (see p. 73 in his 1937 book on the Design of Experiments). For a wonderful account of the history of quantitative geography see Lavalle, McConnell, and Brown (1967).

11. They understand markets for crime as “aggregate units”. In this sense, they merge place with spatial aggregate units of information such as census tracts, although they indeed warn the reader about the conceptual difference between neighborhoods and census tracts (see Footnote 4 in p. 780). In that case, the decision to merge place (neighborhood) with space (census tract) was purely methodological.

12. That is the place of crime.

13. For example see Anselin’s (1999).

14. Spatial patterns sometimes may simply be a statistical nuisance resulting from a regression model suffering from oversimplifying assumptions.

15. Spatial diffusion may be contagious o hierarchical, and operate either by relocation or expansion.

16. Spillover effects are the same as diffusion effects.

17. Most likely inflated as spatial dependence tends to be positive.

18. At a minimum, there is no evidence of violation of OLS assumptions.

19. OLS residuals may be mapped in order to see which places fit the data better or worse.

20. Nonfactual or unsubstantial spatial nonstationarity.

21. Spatial heterogeneity does not seem to depend on sample size.

22. Factual spatial nonstationarity.

23. I am not aware of a previous publication dealing with this issue. One valuable contribution would be a comparative study focusing on the spatiality of crime prevention policy outcomes.

24. For example, when analyzing the persistence of high levels of criminal activity in some places (i.e. endemic crime hotspots) if substantial spatial heterogeneity is found, it may be a spatial effect of (1) lack of synchronicity and/or (2) uneven funding in different areas of policy (e.g. policing, substance abuse treatment, rehabilitation courses, etc.).

25. A parameter is a statistical attribute of an entire population.

26. A spatial kernel is both a measure of density and a method for density analysis. The kernel density function calculates the density of a variable within a radius. A spatial kernel has shape and width (i.e. kurtosis and variance).

27. Under a discrete or dichotomous definition of location, places within each local space are given a weight of “1” and places outside the space are given a weight of “0” (Fotheringham et al., 2002).

28. Note that a traditional OLS model is given when distance is 1 (d = 1).

29. Yet, this might not be the optimal.

30. Not to be confused with the AIC in OLS. Each criterion is calculated in a partially different manner.

31. Notice that typically there are much fewer parameters to be estimated than spatial units or places in the data-set. In the illustration that follows on Canadian provinces, however, the numerical difference between parameters and spatial units is not quite large, meaning that other ways to contrast local models may be more appropriate.

32. Canada has 10 provinces and 3 territories. However, OECD data integrates the Northwest Territories with the Nunavut territory.

33. Due to the small sample size significance cut-off was established at = 0.10 (i.e. 90% level of confidence to reject the null hypothesis of no correlation).

34. Intercepts were also of different sign and magnitude.

35. In the Northwest Territories and Nunavut, both correlates can be expected to have an impact on murder rates.

36. I want to thank one of the reviewers for this observation.

37. Note that GWR also assumes that the model residuals are independently and equally distributed as a standard normal distribution with zero mean and constant variance at each location (Fotheringham et al., 2002; Lu, 2010).

38. Unlike SAM. However, SAM cannot account for spatial heterogeneity.

39. See Fornango’s (2010) paper in this journal for an illustration of spatial regression in crime studies.

Additional information

Notes on contributors

Carlos J. Vilalta

Carlos J. Vilalta is an associate professor at the Center for Economic Research and Education (CIDE) in Mexico City and visiting scholar in the School of Urban Planning at McGill University. He studies the spatial and temporal elements of crime and fear of crime.