Traffic crashes significantly contribute to global fatalities, particularly in urban areas, highlighting the need to evaluate the relationship between urban environments and traffic safety. This study extends former spatial modeling frameworks by drawing paths between global models, including spatial lag (SLM), and spatial error (SEM), and local models, including geographically weighted regression (GWR), multi-scale geographically weighted regression (MGWR), and multi-scale geographically weighted regression with spatially lagged dependent variable (MGWRL). Utilizing the proposed framework, this study analyzes severe traffic crashes in relation to urban built environments using various spatial regression models within Leon County, Florida. According to the results, SLM outperforms OLS, SEM, and GWR models. Local models with lagged dependent variables outperform both the global and generic versions of the local models in all performance measures, whereas MGWR and MGWRL outperform GWR and GWRL. Local models performed better than global models, showing spatial non-stationarity; so, the relationship between the dependent and independent variables varies over space. The better performance of models with lagged dependent variables signifies that the spatial distribution of severe crashes is correlated. Finally, the better performance of multi-scale local models than classical local models indicates varying influences of independent variables with different bandwidths. According to the MGWRL model, census block groups close to the urban area with higher population, higher education level, and lower car ownership rates have lower crash rates. On the contrary, motor vehicle percentage for commuting is found to have a negative association with severe crash rate, which suggests the locality of the mentioned associations.