# Revealing the Spatial Pattern of Weather-Related Road Traffic Crashes in Slovenia
## 3 Results
### The GWR and the Regression Tree Models  
In order to properly fit a Poisson GWR model, all predictor variables were tested for possible multicollinearity. Table 1 indicates that all predictors met the basic criteria since correlation coefficients were within the \(-0.5\) and \(+0.5\) margin [40]. However, low variance inflation factors (VIF \(<3\)) additionally excused further use of these predictors in the modelling procedure. Figure 1: Spatial trends in road traffic crashes: (**a**) all crashes (**b**) rain, (**c**) snow, (**d**) wind, (**e**) fog. At the initial stage, all road traffic crashes (major injury, death) in the time span 2006-2018, regardless of the weather conditions, were considered as the dependent variable. Global Poisson regression results were produced (Table 2) and then compared against the GWR product (Table 3). All predictor variables had a statistically significant impact on the dependent variable (\(p<\alpha\); \(\alpha=0.05\)). From the global regression perspective, all predictor estimates (except CHI) had a positive influence on road traffic crash frequency in Slovenia. However, the Monte Carlo spatial variability test indicated that two predictors (F3 and CHI) had significant spatially varying estimates. Moreover, the summary statistics for the GWR parameter estimates (Table 3) showed that predictor F1 (registered vehicle frequency, number of adult persons, and highway length) also belonged to the same category, since its impact on the dependent variable was positive in some municipalities and negative in others. Despite the relatively high percentage of explained deviance in the global regression (75%), the GWR approach significantly improved model performance. The Corrected Akaike information criterion (AICc) was, in this case, 3.7-times lower. However, as soon as we sought to model the weather-related spatial road traffic crash pattern, the GWR approach yielded poor results (maximum explained deviance = 21%). Here, non-linear \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **F1** & **F2** & **F3** & **MDC** & **CHI** \\ \hline F1 & 1 & 0.01 & 0.04 & 0.15 & \(-\)0.01 \\ \hline F2 & 0.01 & 1 & \(-\)0.02 & 0.48 & 0.02 \\ \hline F3 & 0.04 & \(-\)0.02 & 1 & 0.15 & 0.18 \\ \hline MDC & 0.15 & 0.48 & 0.15 & 1 & 0.24 \\ \hline CHI & \(-\)0.01 & 0.02 & 0.18 & 0.24 & 1 \\ \hline \hline \end{tabular} \(\mathbb{F}1=\) registered vehicle frequency, population (number of adult persons), and highway length; F2 = traffic loads and highway length; F3 = regional road length; MDC = municipality development coefficient; CHI = climate heterogeneity index.  
\end{table} 
Table 1: Predictor variables correlation matrix (Spearman’s correlation coefficient). Figure 2: Road traffic crash hot and cold spots: (**a**) all crashes, (**b**) rain, (**c**) snow, (**d**) wind, (**e**) fog. The regression tree models enabled an adequate estimation of road traffic crash frequency in different weather conditions. Functions within the rpart.plot package in the R environment were used to produce Figure 3. The structure of the decision trees indicates the distinct nature of weather-related road traffic crash footprints in Slovenia. In rainy, snowy, and foggy weather conditions, the F3 predictor (length of regional roads) was the main contributor. Climate heterogeneity had a major impact on the spatial pattern of road traffic crashes that appeared under strong air advection (wind). The second branch was more diverse, but CHI played a major role in three out of four weather situations (rain, snow, fog). However, predictors MDC and F2 (traffic load and highway length) were important decision makers as well: the first of these in the spatial road traffic crash footprints under snowy or foggy conditions, and the second one in cyclonic (rain), convective (rain + wind), and advective (wind) synoptic situations. However, Table 4 summarizes the overall predictor variable importance per weather situation. We reached a much higher explained deviance parameter with the regression tree models compared to that of the GWR.