## 3 Results and Discussion
### Variable Interaction Model  
The critical variables in the data learning model are identified through the variable and normalised significance (Table 5). This is based upon both testing and validation data sets. From the variable interaction model, it can be inferred that the overall effect of the infrastructure is not significantly different for riders of a different gender. However, the critical variables vary and differ by a small proportion in the rank of importance and their relative effect. The Boolean logic presents the most critical variable for males as R\({}_{\text{HLD}}\), and for females as vehicle manoeuvre. The following variables are estimated in the rank of their importance for males, R\({}_{\text{HLD}}\), followed by vehicle manoeuvre, junction location of the vehicle, junction detail, and road location of the vehicle. However, for females, critical variables are vehicle manoeuvre, followed by R\({}_{\text{HLD}}\), junction details, road location of the vehicle, and road type. The importance rank of the rest of the variables is similar; however, their normalised importance values vary slightly. This leads us to conclude that there are specific attributes of the infrastructure that are risky for all cyclists. However, the level of risk that each infrastructure attribute possesses is dependent upon the gender of the rider. The results agree with the findings in the literature. The infrastructural hazards present different levels of risk to the cyclist based upon their gender (see [20; 32]), and that a bad infrastructure design/condition is rated poorly by the cyclists irrespective of their gender (see [23]). The novel variables introduced in the study, i.e., road hierarchy level and direction, are significant variables. It is recommended that these variables be considered in the cyclists' road safety investigations. The sudden change in the road hierarchy requires a shift in how cyclists need to interact with the infrastructure and other road users. Furthermore, the direction of change, i.e., whether the difference in the hierarchy is from a low class of road to a higher level or vice-versa, is a critical externality.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Male**} & \multicolumn{4}{c}{**Female**} \\ \hline \multirow{2}{*}{**R**} & **Variable Importance** & \multirow{2}{*}{**V\({}_{\text{S}}\)**} & \multirow{2}{*}{**N\({}_{\text{S}}\)**} & **R** & **Variable Importance** & \multirow{2}{*}{**V\({}_{\text{S}}\)**} & \multirow{2}{*}{**N\({}_{\text{S}}\)**} \\  & **(Descending Order)** & & & & & **(Descending Order)** & & \\ \hline
1 & R\({}_{\text{HLD}}\) & 0.098 & 100.0\% & 1 & Vehicle manoeuvre & 0.087 & 100.0\% \\
2 & Vehicle manoeuvre & 0.096 & 98.2\% & 2 & R\({}_{\text{HLD}}\) & 0.083 & 95.2\% \\
3 & Junction location of vehicle & 0.094 & 96.8\% & 3 & Junction detail & 0.08 & 91.8\% \\
4 & Junction detail & 0.092 & 94.5\% & 4 & Road location of vehicle & 0.072 & 82.3\% \\
5 & Road location of vehicle & 0.086 & 88.4\% & 5 & Road type & 0.071 & 81.7\% \\
6 & RC 2 & 0.082 & 84.5\% & 6 & RC 2 & 0.07 & 80.9\% \\
7 & Road type & 0.081 & 83.3\% & 7 & Speed limit & 0.069 & 79.1\% \\
8 & Junction control & 0.079 & 80.7\% & 8 & Skidding and overturning & 0.069 & 79.9\% \\
9 & Speed limit & 0.076 & 77.6\% & 9 & RC 1 & 0.067 & 77.2\% \\
10 & R\({}_{\text{HLD}}\) & 0.075 & 77.1\% & 10 & Junction location of vehicle & 0.067 & 76.6\% \\
11 & RC 1 & 0.074 & 75.4\% & 11 & Junction control & 0.066 & 76.1\% \\
12 & Skidding and overturning & 0.067 & 68.4\% & 12 & R\({}_{\text{HL}}\) & 0.065 & 74.4\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: The critical variable significance model for the input variable.