# Road Infrastructure Investment Limits Based on Minimal Accidents Using Artificial Neural Network
## 3 Results and Discussion
### Sensitivity Analysis of ANN Model  
The average variation trend of ARAs with the different predicting variables is presented in Figure 6. The figure is scaled by normalizing the ranges of each input variable (\(X_{i}\)) between [0, 100] and their corresponding ARA outputs (Y) between [0, 100]. Each curve is an average of various curves, as previously described in the methodology. Starting from Figure 6a, it can be observed that the ARA exhibits a positive exponential growth relationship as Freight Movement increases. This trend is in line with previous findings that the number of accidents and fatalities increase as the number of heavy goods vehicles \begin{table}
\begin{tabular}{c c c c c c} \hline
**Input/Variable (\(x_{i}\))** & **Regression (\%)** & **ANN-Garson (\%)** & **ANN-Olden (\%)** & **Average (\%)** & **Overall Rank/11** \\ \hline Freight & 18.21 & 7.74 & 7.88 & 11.28 & 4 \\ Passenger & 16.48 & 9.67 & 1.40 & 9.18 & 8 \\ CNRV & 0.08 & 3.06 & 6.93 & 3.36 & 11 \\ Total ERMI & 14.64 & 11.84 & 7.72 & 11.40 & 3 \\ Total NRII & 14.63 & 8.29 & 20.45 & 14.46 & 1 \\ ERMI Per Capita & 0.42 & 12.68 & 14.57 & 9.22 & 7 \\ NRII Per Capita & 1.14 & 7.73 & 22.94 & 10.60 & 5 \\ Population & 16.87 & 5.86 & 8.99 & 10.57 & 6 \\ Proportion of Work Group & 0.08 & 6.04 & 5.18 & 3.77 & 10 \\ Population of Work Group & 16.77 & 18.23 & 1.52 & 12.17 & 2 \\ GDP & 0.68 & 8.86 & 2.43 & 3.99 & 9 \\ \hline \end{tabular}
\end{table} 
Table 5: Relative influence/importance ranking of variables. and trucks per capita increase [50; 51]. It should be noted that none of these studies reported the specific nature of the ARA-Freight relationship. In addition, it can be deduced that eliminating the Freight Movement from roads (even if possible) can only enable the lowering of the ARA to a certain cap (not zero). On the other hand, the ARA increases linearly as passenger movement increases (positive linear relationship), but there is a non-zero intercept on the passenger movement axis. This observation is also in agreement with reports on the effect of passenger exposure expressed as vehicle kilometer travel [52] and gasoline sales [53] on the accident rate. A less significant logarithmic growth relationship between ARA and CNRV was also observed. These first three observations (for freight, passenger, and CNRV) are very clear and can be easily understood. The same cannot be said regarding the next four variables related to new road infrastructural investments and existing road maintenance investments (total NRII, total ERMI, NRII/capita, and EMRI/capita). Generally, the ARA decreases to a certain extent with the increase in these predicting variables; then, the ARAs begin to rise as the variables increase further. This means that monetary investment in new road infrastructure or existing road maintenance could result in either a decrease or increase in ARAs, depending on the amount invested. It also explains some of the anomalies on the effects of road investments on ARA variables, as reported by previous studies such as [31; 52; 53]. According to the trends seen here, an average nonlinear concave-up relationship exists, between ARA and new road infrastructure and existing road maintenance investment. The drop and rise in the ARA due to increased maintenance investment is not as pronounced as in the case of new road capital investments. The NRII curves are basic cases of constant demand (fixed freight and passenger movement) and increasing supply (additional road infrastructure). Moderate to low NRII levels will improve the system efficiency by decongesting the overall traffic. This means lesser volume, which leads to a decrease in the level of crash frequency [54]. However, high NRII will not only eliminate congestion, but will also result in a significant increase in the system-wide average speed. The accident rate was found to increase with a higher mean speed for all types of roads [55].