Theorizing globally, but analyzing locally: the importance of geographically weighted regression in crime analysis

Andresen, Martin A.

doi:10.1186/s40163-022-00173-0

Table 3 Geographically weighted regression and global regression results, all crime types

From: Theorizing globally, but analyzing locally: the importance of geographically weighted regression in crime analysis

Variable (expected sign)	Commercial burglary				Residential burglary				Theft from vehicle
Variable (expected sign)	Min	Max	Global	% sig., GWR	Min	Max	Global	% sig., GWR	Min	Max	Global	% sig., GWR
Unemployment rate ( +)	0.020	0.104	0.103	0	− 0.139*	0.097	− 0.046	11.4%	− 0.048	0.116	0.055	0
Population change, % ( +)	0.012*	0.021	0.016*	71.4	0.004*	0.015	0.008*	46.7%	0.010*	0.016	0.010**	100
Rented, % ( +)	− 0.031	− 0.009	− 0.016	0	− 0.059*	− 0.040	− 0.048**	100%	− 0.028*	− 0.016	− 0.014	7.6
Major repairs, % ( +)	− 0.206*	− 0.130	− 0.154*	40.9	− 0.115*	− 0.074	− 0.088*	68.6%	− 0.225*	− 0.198	− 0.163**	100
Old houses, % ( +)	− 0.041	− 0.011	− 0.028	0	− 0.006*	0.052	0.018	35.2%	− 0.005	0.011	0.001	0
Move, 1 year, % ( +)	0.001	0.042	0.037	0	− 0.009	0.043	0.014	0%	− 0.020	− 0.004	0.004	0
Post secondary, % ( −)	− 0.021	0.026	− 0.004	0	− 0.010	0.031	0.003	0%	− 0.004	0.018	− 0.003	0
Low income, % ( +)	0.035*	0.094	0.021	28.6	0.024*	0.044	0.038*	32.4%	0.046*	0.089	0.031	100
Government assistance, % ( +)	− 0.133*	− 0.060	− 0.097	20.9	− 0.111*	− 0.023	− 0.062*	40.9%	− 0.102*	− 0.044	− 0.073**	61.9
Average dwelling value, 000 s ( −)	− 0.001	0.000	0.000	0	0.000	0.000	0.000	0%	− 0.001*	0.000	0.000*	100
Average rent, 00 s ( −)	− 0.093	0.092	− 0.026	0	− 0.139*	− 0.067	− 0.111**	55.2%	− 0.047	0.075	− 0.017	0
Median family income, 000 s ( −)	− 0.028	− 0.006	− 0.023	0	− 0.005	0.002	− 0.001	0%	− 0.013	0.009	− 0.003	0
Aboriginal, % ( +)	− 0.027	0.016	0.034	0	0.021*	0.084	0.055*	15.2%	− 0.002	0.029	0.027	0
Immigrants, % ( +)	− 0.049	− 0.002	0.008	0	− 0.026*	0.052	0.010	5.7%	− 0.047*	− 0.027	− 0.017	23.8
Recent immigrants, % ( +)	− 0.072	0.113	0.043	0	− 0.058	0.013	0.026	0%	0.015	0.063	0.038	0
Visible minorities, % ( +)	− 0.040	− 0.004	− 0.031	0	− 0.028	0.018	− 0.007	0%	− 0.006	0.008	0.001	0
Ethnic heterogeneity ( +)	− 0.009*	0.040	0.013	28.6	− 0.015	0.005	0.000	0%	0.001	0.014	0.002	0
Wald of F-statistic			9.29**				19.9**				36.94**
Leung et al. (2000)	p-value = 0.31				p-value = 0.17				p-value = 0.21
AIC	231.2		267.4		74.4		126.9		124.2		145.1
GWR Quasi-global R²	0.72				0.76				0.70
OLS (Adjusted) R²			0.62 (0.55)				0.60 (0.52)				0.59 (0.51)
Global model			Lag				Error				Lag
Spatial weights			1				1				1
Moran’s I, residuals p-value	0.15		0.72		0.08		0.38		0.07		0.98
Koenker’s test for heteroskedasticity, p-value			0.59				0.91				0.36

Variable (expected sign)	Theft of vehicle				Other theft
Variable (expected sign)	Min	Max	Global	% sig., GWR	Min	Max	Global	% sig., GWR
Unemployment rate ( +)	− 0.129	− 0.041	− 0.073	0	− 0.381	− 0.150	− 0.171	0
Population change, % ( +)	0.007*	0.012	0.009**	50.5	0.020	0.025	0.023*	0
Rented, % ( +)	− 0.027	− 0.017	− 0.017	0	− 0.080	− 0.025	− 0.051	0
Major repairs, % ( +)	− 0.105	− 0.093	− 0.080	0	− 0.394**	− 0.239	− 0.339	40.9
Old houses, % ( +)	− 0.004	0.007	− 0.001	0	0.008	0.060	0.026	0
Move, 1 year, % ( +)	− 0.006	0.003	0.003	0	− 0.024	0.025	0.007	0
Post secondary, % ( −)	− 0.017	− 0.006	− 0.015	0	0.020	0.054	0.032	0
Low income, % ( +)	0.038*	0.059	0.030	83.8	0.016	0.111	0.064	0
Government assistance, % ( +)	− 0.098*	− 0.063	− 0.072**	67.6	− 0.199	− 0.072	− 0.151	0
Average dwelling value, 000 s ( −)	− 0.001*	− 0.001	− 0.001**	100	− 0.002*	− 0.001	− 0.001*	39.1
Average rent, 00 s ( −)	− 0.066	− 0.015	− 0.029	0	0.069	0.326	0.150	0
Median family income, 000 s ( −)	− 0.002	0.007	− 0.001	0	− 0.079*	− 0.049	− 0.058*	28.6
Aboriginal, % ( +)	0.045	0.071	0.055*	0	− 0.060	0.114	0.066	0
Immigrants, % ( +)	− 0.040	− 0.025	− 0.022	0	− 0.108	− 0.061	− 0.088	0
Recent immigrants, % ( +)	0.044	0.056	0.051	0	0.003*	0.271	0.182	3.8
Visible minorities, % ( +)	0.011	0.019	0.009	0	0.010	0.076	0.037	0
Ethnic heterogeneity (+)	− 0.007	0.001	− 0.003	0	− 0.042	0.047	0.006	0
Wald of F-statistic			8.49**				F = 3.49**
Leung et al. (2000)	p − value = 0.43				p − value = 0.46
AIC	133.6		158.5		376.9		408.9
GWR Quasi-global R²	0.62				0.54
OLS (Adjusted) R²			0.56 (0.48)				0.41 (0.29)
Global model			Lag				OLS
Spatial weights			1				1
Moran’s I, residuals p-value	0.13		0.86		0.26		0.17
Koenker’s test for heteroskedasticity, p-value			0.41				0.04

^* p < 0.05, ** p < 0.01. The OLS model for Other Theft reports statistical significance with robust standard errors because of the presence of heteroskedasticity

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