Smallest is Better? The Spatial Distribution of Arson and the Modifiable Areal Unit Problem

Abstract

Objectives

The aim of this study is to explore how the zonation and scale problems of the modifiable areal unit problem (MAUP) impact on the proportion of variance associated with surrounding areas in relation to micro-place levels of arson. MAUP is related to how geographical areas are constructed, with zonation related to how boundaries are drawn, and scale related to the size of areas.

Methods

Arson point data from 2007 to 2011 are analyzed by means of hierarchical linear modeling in order to compute intra-class correlations (ICCs), the share of variance associated with the higher order geographical units, for geographical units of three different sizes and with three degrees of randomness. Real, administrative, geographical units of two sizes, with mean size of 1.2 and 0.4 square kilometers respectively, are compared both to semi-random and fully-random artificial geographical units of the same size, and to smaller types of units of 0.17 square kilometer size.

Results

The analysis shows that there is little difference between large and medium-sized geographical units, but there is a significant increase in the ICC at the smallest geographical scale. To understand the geography of arson this suggests that the smallest types of units are of the greatest importance. As regards the problem of zonation, the results show that more randomness of boundary placement is associated with lower ICCs.

Conclusion

A key implication of these findings is that community preventive efforts may best be targeted at very small communities such as street blocks rather than larger neighborhoods.

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Notes

  1. 1.

    The term modifiable in MAUP can be said to be linked to the lack of a connection between studied social mechanisms and the geographical units of analysis employed in analyses (Flowerdew 2011). The problem is related to the widespread use of administrative units of analysis both in criminology, and more broadly in the social sciences (Sampson et al. 2002).

  2. 2.

    This is also related to the discussion of whether social disorganization-based theories (cf. Sampson et al. 1997) or opportunity based theories (Cohen and Felson 1979) are best suited to understanding crime at micro-places, as discussed by Braga and Clarke (2014; see also Weisburd et al. 2012).

  3. 3.

    Some social disorganization scholars may however disagree. Robert Sampson touches on the issue: “The notion that there is one neighborhood unit or that it must be small is not commensurate with the way people react to and sort themselves on a wide variety of dimensions or outcomes” (Sampson 2012: 362).

  4. 4.

    Hipp and Boessen (2013) attempt to integrate large and small scales of geographical perspectives by employing overlapping egohoods (Hipp and Boessen 2013), where each street block is influenced by street blocks in concentric circles, each of which is in turn influenced by street blocks radiating out in concentric circles from itself. It was found that egohoods were better suited for understanding the spatial distribution of crime than administrative units of analysis.

  5. 5.

    Brantingham et al. (2009) used a method for assigning places varying degrees of membership in neighborhoods in order to better understand the spatial clustering of crime.

  6. 6.

    The definition of arson broadly corresponds to the definition employed by Drucker (2011, 29): “Arson is defined as any fire of an incendiary or suspicious origin.”

  7. 7.

    As discussed in Steenbeek and Weisburd (2015) street segments, commonly used to operationalize micro-places, often belong to more than one census tract, making such spatial analysis difficult. There are however papers that have assessed the problem of scale in the form of individuals nested in different sized geographical units of analysis, rather than places nested within places. Hipp (2007), for example, examined crime outcomes, while Oberwittler and Wikström (2009) examined outcomes related to cohesion and informal social control. For an overview of related research of primarily non-criminological outcomes, see Matthews and Yang (2013).

  8. 8.

    One study found that respondents tended to consider crimes within a half mile radius when asked about crimes in their neighborhood, but with large variations depending on the type of offence (Wisnieski et al. 2013). Studies allowing respondents to draw their neighborhoods on a map have reported differing results in terms of the size of neighborhoods. Orford and Leigh (2014) found that, on average, neighborhoods were defined to be of a size similar to Output Areas, an administrative geographical unit with an average of 300 residents, while Coulton et al. (2001) found that perceived neighborhoods were comparable to census tracts, with an average of 2589 residents.

  9. 9.

    Zonation is arguably a better term than the original term aggregation used by Openshaw (1984).

  10. 10.

    A recent paper has added the concept of the uncertain geographic context problem (UGCoP) to the discussion of contextual effects on individual outcomes (Kwan 2012). UGCoP is concerned with the problem of delineating geographical units of analysis when the actual geographical unit that best matches the context to be studied is unknown. It largely encompasses the zonation issue aspect of the MAUP, but also widens the discussion to include essentially non-geographical contexts such as friendship networks and brings a temporal aspect of exposure to the table (Kwan 2012). Although this paper is not concerned with contextual effects on individuals, the solution to the delineation of geographical units of analysis problem that Kwan (2012, 965) discusses is taken into account in this paper by employing GPS data to attempt to establish better delineation.

  11. 11.

    See also Wikström et al. (2012), however, for a study using smaller geographical units of analysis and Sutherland et al. (2013) for a discussion.

  12. 12.

    In Weisburd et al. (2012), attempts are made to identify variables related to social disorganization at the micro-level, in addition to variables related to opportunity theory, by measuring structural characteristics of social disorganization such as SES rather than actual social mechanisms (see also Ouimet 2000).

  13. 13.

    The trend towards smaller scales of geography is also being driven by technological and methodological innovations, as discussed by Weisburd et al. (2009a).

  14. 14.

    Research on the spatial distribution of arson in Sweden has revealed that it is strongly correlated at the neighborhood level to poor living conditions as measured using a summative standardized index of the number of residents per room, the proportion of young men aged 16-18, the proportion of residents with no more than 9 years of school education, the proportion of foreign-born residents and the proportion of unemployed aged 18–64 (Guldåker and Hallin 2013; Hallin et al. 2010). This living conditions variable shares some constituent elements with the concept of concentrated disadvantage, and the theoretical reasoning behind it is similar (cf., Sampson et al. 1997; Sampson 2012). Malmberg et al. (2013) have found that incidents of car arson as a measure of rioting are related to residential (ethnic) segregation, the proportion of youth and the proportion of parents on welfare.

  15. 15.

    Administrative medium-sized areas that are adjacent to the sea in the western section of the city have boundaries drawn far out into the sea. For the present paper, only those parts of SAMS-areas falling within the municipality have been used, which has been achieved by simply clipping the SAMS-areas with the sub-districts.

  16. 16.

    This is related to a difference in the Swedish language between a fire that is controlled/wanted (“eld”) and a fire that is out of control/unwanted (“brand”), where the fires used in this paper can be considered fires where the intent was to start a fire that would become out of control (“Brand anlagd med uppsåt” in Swedish).

  17. 17.

    The Swedish police classify incidents of arson into three principal offence categories; vandalism; carelessness endangering the public through arson; (Translations from Rikskriminalpolisen 2002); and endangering human lives through intentional arson.

  18. 18.

    The centroid of the pixel thus determined which geographical unit of analysis it would be assigned to. This may result in a slight misrepresentation of the number of arsons across level 2 units in some cases, but there is no reason to believe it would systematically impact on a comparison across different sets of geographical units of analysis.

  19. 19.

    The resulting tables have slightly differing numbers of points depending on the exact boundaries drawn for the randomly created geographical units of analysis. For large sized randomly generated units, this resulted in between 64,536 and 64,544 artificial micro-places and for medium sized randomly generated units between 64,540 and 64,542. Administrative large areas were registered for 64,574 artificial micro-places and administrative medium areas were registered for 64,542 points.

  20. 20.

    In relation to the MAUP, this is similar to the technique suggested by Tranmer and Steel (2001) to assess scale effects by calculating what they call intra-area correlations (IACs) by dividing the higher order unit variance with the lower order unit variance.

  21. 21.

    For the output-area-sized units, this results in a mean population of 323, as compared to the 300 in Wikström et al. (2012).

  22. 22.

    An example can be seen in Fig. 3, where the biggest area in the large administrative set, the easternmost area in Fig. 3g, is bigger than any artificial unit.

  23. 23.

    Attempts at fitting the models were performed using the overdispersed poisson distribution in HLM 6, the negative binomial distribution in STATA 13, and, after recoding the outcome variable into a dichotomous variable, using Bernoulli distribution in HLM6.

  24. 24.

    The linear mixed models also fail to meet assumptions of normality at level 2, but the lack of normality is similar across the data-sets making comparison more viable. Recent research shows that negative binomial mixed models perform better than linear mixed models with raw data, but the linear mixed model performed as well or better for some specifications (Aly et al. 2014). In the present paper the models are however overdispersed, which tend to fit better with negative binomial models. The non-normality at level 1 is the same across all 62 level 2 units, and should have little impact on comparisons between different level 2 units. It does however mean that ICC-values as measures of actual variance should be interpreted with caution.

  25. 25.

    Confidence intervals based on t-distribution, with 9 degrees of freedom.

  26. 26.

    There are no substantive differences between the results reported in (Appendix) Table 3 where the proportion of built-up land is controlled for and the results from empty models. Empty model results available on request. It should however be noted that these results are based on a differing number of level 2 units due to the heterogeneity in the data, and the number of level 2 units included in the analysis is reported in the table.

  27. 27.

    Sampson (2012) also noted that the size of geographical units appeared to have a minor impact when comparing neighborhood clusters with on average 8000 residents with smaller census tracts. Chicago census tracts however have a similar mean number of residents as the largest type of units studied in the present study. The findings in this paper are thus in line with Sampson (2012) while also noting that even smaller scales of geography may be of larger importance.

  28. 28.

    A similar argument has been made by Bernasco (2010, 115): “In the absence of well-defined boundaries between spatial units, the measurement of small entities is to be preferred, even if the mental maps of the users are less fine-grained.”

  29. 29.

    Although both opportunity and social disorganization theoretical explanations were discussed by Baudains et al. (2013), the authors found that crime pattern theory (cf. Brantingham and Brantingham 1995) made the largest contribution to a spatial understanding of the riots.

  30. 30.

    Of the ten artificial micro-places in this study with more than 10 instances of arson during the period examined, four are in places where there have been several instances of clashes with the police. In addition, two of the remaining six artificial micro-places with more than 10 instances of arson are located at schools in disadvantaged neighborhoods.

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Correspondence to Manne Gerell.

Appendix

Appendix

See Tables 3, 4 and Fig. 5.

Table 3 Descriptive geographical statistics for sets of geographical units used given in meters/square meters
Table 4 ICC-values for different geographical units of analysis after removing all level 2 units with a mean number of micro-place arsons below 0.05
Fig. 5
figure5

Kernel density, 500 m radius, of arson registered by rescue services 2007–2011 in the city of Malmö

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Gerell, M. Smallest is Better? The Spatial Distribution of Arson and the Modifiable Areal Unit Problem. J Quant Criminol 33, 293–318 (2017). https://doi.org/10.1007/s10940-016-9297-6

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Keywords

  • Arson
  • MAUP
  • Neighborhood
  • Geography