## Materials and Methods
### Phase-II: Application of ANNs Model for Risk Prediction and Evaluation
The model giving the best validation statistic was chosen as the final model. This method was best for small data sets because it made efficient use of limited amounts of data [57; 58].The ANN based predicted value of risk was mapped in the GIS environment as shown in Figure 4, showing a red line as the riskiest segments, while dark green segments are the safest as there zero crashes on these segments. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{2}{l}{**Estimates-Hidden Layer**} & \multicolumn{1}{l}{**H1\_2**} & \multicolumn{1}{l}{**H1\_3**} & \multicolumn{1}{l}{**H1\_4**} \\ \cline{2-6}  & **Code** & **H1\_1** & **H1\_2** & **H1\_3** & **H1\_4** \\ \hline
**Flow** & & 0.258908 & \(-\)2.00717 & 0.868246 & 4.984629 \\
**Speed** & & \(-\)1.26756 & 3.435496 & \(-\)1.83834 & 2.048267 \\
**Horz\_Curve** & 0 & 2.150204 & 13.66468 & \(-\)1.03056 & 1.968045 \\
**Vert\_Curve** & 1 & 2.141838 & \(-\)2.07175 & 1.313892 & 0.014534 \\
**Intercept** & 2 & \(-\)3.21511 & 7.986301 & \(-\)3.09312 & \(-\)0.53461 \\
**Intercept** & & 1.90514 & \(-\)1.87443 & 0.481882 & \(-\)4.76064 \\ \hline  & **Int** & **H1\_1** & **H1\_2** & **H1\_3** & **H1\_4** \\ \hline
**NLog\_Risk** & 2.221 & \(-\)2.34861 & 6.612427 & \(-\)1.8978 & 2.041027 \\ \hline
**Cross Validation** & & & & & \\ \hline
**Sample Size** & **Training** & 53 & **Validation** & 14 & \\
**R\({}^{2}\)** (Training) & 0.788 & **R\({}^{2}\)** (Validation) & 0.775 & **RMSE** & 0.624 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parametric estimates of the ANNs Model. Figure 4: Geographical information system (GIS)-based ANNs-predicted risk spatial map. The values of R-square and Root Mean Square Error (RMSE) are the two basic validation indicators for testing the goodness-of-fit of the model. ANNs is a very flexible model and has a tendency to overfit data. When that happens, the model predicts the fitted data very well, but predicts future observations poorly. To mitigate overfitting, the neural platform applies a penalty on the model parameters and uses an independent dataset to assess the predictive power of the model. The applied technique to control overfitting is the squared method. This method is applied if it is considered that independent variables are contributing to the predictive ability of the model. During the analysis, the graphical representation of data showed a better performance both in the case of training and validation data. The data distribution was adopted in five segments, having a distribution of 53 segments for training and 14 segments for validation. The plots showing the perfection of predictability were shown in Figure 5 for both training and validation data. The values of R-square were also almost similar for both major and training and validation data sets. The contribution of factors associated with risk can be analyzed by the importance of the variables (i.e., Flow, Speed, Vertical and Horizontal Curve).The impact of variables is one of the necessary targets to analyze and improve the safety performance of the roads. Traffic safety engineers always search for the relationships between factors and safety performance indicators (i.e., Risk). The relationship can be observed in Table 5, which shows that speed and flow were two major factors which are having a high impact on risk. A comprehensive analysis to overview the importance of factors provides traffic engineers to take a decision during road safety analysis and implementation procedure.