A visual approach for defining the spatial relationships among crashes, crimes, and alcohol retailers: Applying the color mixing theorem to define the colocation pattern of multiple variables

In traffic safety studies, the few scholars who have focused on analyzing disaggregated data obtained results that have been either difficult to explain or demonstrate because they did not provide clear visual maps or utilize statistical tests to quantify the spatial relationships. In order to increase the use of such disaggregated spatial methods for use in traffic safety studies, the current study documents the application of a new RGB (red, green, blue) model which combines the color additive theorem and the kernel density map (KDE) to define crash colocation patterns and the coincidence spaces of related variables. This study contributes to the literature in three major ways: (1) a new RGB model was established and applied in the field of traffic safety; (2) the variable dimensions were expanded from two to three; and, (3) the dimension of uncertainty was also included. When the new RGB model was utilized with data collected in College Station, Texas, the results indicated that the new colocation map is able to clearly and accurately define colocation hotspots of crashes, crimes, and alcohol retailers. As expected, these hotspots are located in areas with many bars, the largest strip malls and busiest intersections. The intensity maps have provided results consistent with the above colocation maps. However, the uncertainty map does not show a relatively higher level of certainty regarding the location of hotspots as we expected because the input of each variable was not related to the highest kernel value. Therefore, future scholars should focus on the colocation and intensity maps while using the uncertainty map as a reference for individual event risk evaluation only.