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Residential Burglaries and Neighborhood Socioeconomic Context in London, Ontario: Global and Local Regression Analysis*

2005; Routledge; Volume: 57; Issue: 4 Linguagem: Inglês

10.1111/j.1467-9272.2005.00496.x

1467-9272

Jacek Malczewski, Anneliese Poetz,

Urban, Neighborhood, and Segregation Studies

Abstract The main aim of this article is to analyze the relationships between the spatial patterns of residential burglaries and the socioeconomic characteristics of neighborhoods in London, Ontario. Relative risk ratios are applied as a measure of the intensity of residential burglary. The variation in the risks of burglary is modeled as a function of contextual neighborhood variables. Following a conventional (global) regression analysis, spatial variations in the relationships are examined using geographically weighted regression (GWR). The GWR results show that there are significant local variations in the relationships between the risk of residential burglary victimization and the average value of dwellings and percentage of the population in multifamily housing. The results are discussed in the context of four hypotheses, which may explain geographical variations in residential burglary. The practical implication of the GWR analysis is that different crime prevention policies should be implemented in different neighborhoods of the city. Key Words: residential burglaryneighborhood socioeconomic characteristicsglobal and local regression analysisLondonOntario Notes Source: Statistics Canada 2002. Note: Variables in bold are significant at the 5 percent level. *minimum AIC value. Note: R 2=0.202; Shapiro-Wilks normality test on residuals: 0.951, prob. 0.000; Moran's I on residuals: 0.438, prob. 0.001. Note: OLS=ordinary least squares; SS=sum of squares; MS=mean sum of squares; R 2=0.590. Note: Variables in bold are significant at the 5 percent level. *optimal bandwidth. Note: and are the average values of the x 2 and x 7 variables for all EAs; RR i is the relative risk of residential burglary (see Note 1). 1 The relative risk (RR i ) ratio is defined as follows (CitationBailey and Gatrell 1995): RR i =100(o i /e i ), where is the expected number of burglaries in the i-th EA in 1998–2001, o i is the observed number of residential burglaries in the i-th EA in 1998–2001, and p i is the "population at risk" (the number of dwellings) in the i-th EA in 1999. If the RR i values are less than 100, then EA is characterized by relatively low risk (that is, the risk is less than expected for the study area). The RR i values greater than 100 indicate that the risk is greater than expected. 2 The global multiple regression model has the following form: , where y i represents independent variable at the i-th EA (i=1,2,…,m), which is a function of n parameters β 0 and β k (k=1,2, …, n−1) and (n−1) contextual explanatory variables x ik ; the ϵ i 's are independent normally distributed, unobserved error terms (or residuals) with zero mean and constant variance. The ordinary least squares (OLS) method is typically employed to estimate the parameters (see, e.g., CitationMiller 1990; CitationSelvin 1998). The method is based on a set of assumptions such as normality, homogeneity of variance, and independence of residuals. Spatial autocorrelation (or spatial dependency) and spatial nonstationarity (spatial heterogeneity) are two properties of spatial data that may undermine the assumptions behind the traditional regression models (see, e.g., CitationBailey and Gatrell 1995). 3 The GWR model is an extension of the global multiple regression (see Note 2). It has the following form: , where β i0 and β ik are the values of the parameters at the i-th location. To calibrate the model, a modified, weighted, least squares approach is used so that the data are weighted according to their proximity to the i-th location. Data from observations closer to i are weighted more heavily than those farther away. Hence, the estimator for the parameters in GWR can be expressed in the matrix format as follows: , where W i is an m×m matrix (the diagonal elements of the matrix denote the geographical weighting of observed data for the i-th location and off-diagonal elements are zeros) (CitationFotheringham, Charlton, and Brunsdon 2002). The GWR procedure provides us with all elements and diagnostics of a global regression model including parameter estimates, goodness-of-fit measures, and t-values on a local basis. One advantage of the GWR modeling is that it addresses the problem of spatial nonstationarity directly (CitationBrunsdon, Fotheringham, and Charlton 1996; CitationFotheringham, Charlton, and Brunsdon 2002). Also, there is empirical evidence to show that, usually, the residuals obtained from GWR do not exhibit any spatial pattern (see CitationFotheringham, Charlton, and Brunsdon 2002). The present study is consistent with this finding. Further discussion of the advantages and disadvantages of the GWR modeling can be found in CitationLeung, Mei, and Zhang (2000a, b) and CitationPáez, Uchida, and Miyamoto (2002a, Citationb). 4 A fixed Gaussian kernel function has the following form: w ij =exp⌊−(d ik /α)2⌋, where α is the bandwidth and d ik is the distance between location i and k. Alternatively, an adoptive bandwidth can be used. In this case, the following bi-squared function can be implemented: w ij =[1−(d ik /α)2]2, if d ik ≤α, and w ij =0, if d ik >α (CitationFotheringham, Charlton, and Brunsdon 2002). Although the findings reported in this article are based on the implementation of GWR with a fixed kernel, we have also used GWR with an adoptive kernel. The results produced by GWR with the two weighting functions are very similar. For example, the AIC values are: 4942.1 and 4939.8 for optimal fixed and adoptive kernels, respectively. There are only two variables (x 2 and x 7 ) in the GWR models with optimal fixed and adoptive bandwidths that are statically significant at the 5 percent level. The spatial patterns of the t-values for x 2 and x 7 produced by the GWR model with an optimal fixed kernel (see Figures 3 and Figure 4) are very similar to those obtained for an optimal adoptive kernel. 5 It is also important to examine casewise diagnostics such as the local R 2 statistics, standardized residuals, and influence statistics. The local R 2 values are in the range from 0.445 to 0.779, indicating that the models calibrated at the regression points (EAs) replicate the data in the vicinity of that point reasonably well. The standardized residuals provide another set of casewise diagnostic measures that can be used to identify unusual cases (EAs). For the GWR model, the values of the standardized residuals range from −2.401 to +2.769. More then 95 percent of the standardized residuals are between −2.58 and +2.58, indicating that the distribution of residuals is approximately normal. It is also important that we know whether individual cases exert a significant effect on the results. The Cook's distance provides a suitable measure (CitationFotheringham, Charlton, and Brunsdon 2002). For the GWR model, the maximum value of the Cook's distance is 0.044. This small value of the measure indicates that there are no unusual cases in terms of the dependent or independent variables (see, e.g., CitationMiller 1990). *The authors would like to thank the London Police Department for generously providing their data and anonymous reviewers for their valuable suggestions and helpful comments on the manuscript. All errors remain those of the authors. Additional informationNotes on contributorsJacek Malczewski An Associate Professor Anneliese Poetz A PhD student