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Exploratory Regression Analysis
The result of our exploratory analysis shows that the best model to be selected for OLS and GWR analysis are the following factors: percent of housing crowded, percent aged 16+ unemployed, and percent aged 25+ without high school diploma. This model was chosen because they form the strongest relationship with the highest AdjR2 value (0.31) and the lowest AICc value (800.62) among all other model options. Among the three factors, percent of housing crowded, and the percent 16+ unemployed yield positive relationships with the occurrence of weapon violation while percent 25+ without high school diploma shows a negative relationship.
Fig.8 Exploratory Regression Analysis result
Ordinary least squares (OLS)
The result of the ordinary least square (OLS) suggests that higher percentage of crowded housing is associated with higher rates of weapon violations. Similarly, higher percentage of unemployed population above the age of 16 is also positively correlated with the occurrence of weapon offences. However, as a global trend, higher percentage of population without high school diploma above 25 is found to have a negative relationship with the number of weapon violations in the city of Chicago.
Table 6. Summary of OLS coefficient of the relationship between socio-economic variables and weapon violations.
Geographically weighted regression (GWR)
The geographically weighted regression model (GWR) is increasingly being used as an exploratory technique for spatial prediction in a variety of contexts such as social science and life science. The GWR output surfaces illustrate the spatial variation of the coefficient values, creating a visual representation of the positive or negative association of each parameter with the occurrence of weapon violations.As observed in panel A of Figure 9, the south side of Chicago (Oakland, Grand Boulevard and Kenwood), along with a small central region (downtown Chicago) display the strongest positive relationship between the percentage of crowded housing and the number of weapon violations. The positive relationship (shown in red) extends towards the southwest and a part of the west side of the city, but to a less extent. On the other hand, the far southwest, far southeast and the northwest side of the city exhibit a negative relationship.
Panel B shows the relationship between the percentage of unemployed population above the age of 16 and the number of weapon violations. Overall, the entire city of Chicago displays positive association between unemployment and the occurrence of weapon offence, with inter-community variation in terms of the intensity of the correlation. It was found that the strongest positive correlation is predominantly concentrated in the far northwest corner of Chicago (especially Dunning); the positive relationship appears to be less pronounced along the east border of the city, extending down towards the far southeast side.
The relationship between the percentage of above the age of 25 without high school diploma and the occurrence of weapon violations are seen in panel C. An interesting pattern can be observed, where the city was virtually separated into three parts based on its GWR coefficient values. The far southwest and far southeast side of Chicago demonstrates the strongest positive correlation (especially Washington Heights and Chatham) while the south and southwest region show the strongest negative correlation (especially Oakland) between the factor and the occurrence of weapon offence. In the west side of the city (namely Humboldt Park and Austin), the percentage of population above the age of 25 without high school diploma is slightly positively associated with the number of weapon violations.Comparing the GWR coefficient surfaces, it can be observed that panel A exhibits the greatest range between the highest (26.79) and the lowest coefficient value (-5.48). Panel B only shows positive relationship throughout the city with relatively lower variation in range in the intensity of the relationship.
Fig. 9 GWR and coefficient surfaces of independent socioeconomic variables on weapon violations
Hardship Index GWR Coefficient Surface Overlaid by Individual Socio-economic Index Coefficient Point Layers
It can be seen from the colour ramp on the hardship index coefficient in Figure 10 that the hardship index is generally positively associated with the number of weapon violations in Chicago. The far southwest region of the city exhibits the most pronounced positive relationship (red), which is partly contributed by the factor of unemployment and education (red coefficient dots in the same area).The far southeast and the northeast regions displayed relatively weaker relationship. The crowded housing variable appears to have been a contributing factor for the weak positive relationship observed in the southeast end of the city.
Fig. 10 GWR of Hardship Index overlaid by individual index coefficient point layers