## 6 Human Perception of Severity and Objective Measures
**Model development**: A model focused on human perception was created to assess the relationship between the human judgement of severity and surrogate measures. Five trained observers were asked to rank the perceived danger levels of interactions, classifying \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Phase** & **Definition** &
\begin{tabular}{c} **Time Instance** \\ **Notation** \\ \end{tabular} & **Indicators** & **Included in the Model** \\ \hline \multirow{2}{*}{Preliminary Stage} & The moment when first evasive action was taken. & EA & EA, \(T_{2}\), \(D_{R}\), V & D \\ \hline \multirow{4}{*}{Peak Stage} & The point in time when T\({}_{2}\) reaches its lowest value in the event. & \(T_{2}^{min}\) & \(T_{2}\), \(D_{R}\), V, \(D_{1}\), \(D_{2}\) & A, B, C, D \\ \cline{2-6}  & When the travel-to-collision-point distance of each road user reaches its minimum value during the interaction. & \(D_{2}^{min}\) & \(T_{2}\), \(D_{R}\), V, \(D_{1}\), \(D_{2}\) & A, B, C, D \\ \hline \multirow{4}{*}{End stage} & The point in time when the first road user arrives at the potential conflict zone. & \(T_{1}\) & \(T_{2}\), \(D_{R}\), V, \(D_{1}\), \(D_{2}\) & A, B, C, D \\ \cline{2-6}  & The point in time when the second road user reaches the potential collision zone. & \(T_{2}\) & PET & A, B, C, D \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Moments for calculating objective measures. Figure 6: Key moments during various vehicle interactions were considered for estimation of objective measures in this study. them as either safe, mild or severe. These ratings were collected using a Likert scale, which is an ordinal scale, meaning that the response variable had more than two categories and these categories had a predefined order. Therefore, an ordinal logistic regression model was used to develop this model. Equation (2) of ordinal logistic regression can be expressed as below [44]:  
\[\text{logit}\left[P(y\leq j)\right] =\log\left[\frac{P(y\leq j)}{1-P(y>j)}\right]=\alpha_{j}+\beta_{1}X_{ 1}+\beta_{2}X_{2}+\ldots\ldots+\beta_{k}X_{k},j=1,2,3\ldots,c-1\] (2) where:  
\(y\) = response variable;  
\(X_{1}\), \(X_{2}\),... \(X_{k}\) = explanatory variables;  
\(c\) = number of categories for response variable;  
\(P(y\leq j)=\) cumulative probabilities for \(jth\) category. \(P\) (y > j) = probability that y is greater than j;  
\(\alpha_{j}\) = intercepts parameter;  
\(\beta\) = parameters related to explanatory variable. This study used the maximum likelihood approach to fit all of the logistic regression models. This test uses a chi-square distribution with n-k-1 degrees of freedom, where n represents the sample size and k represents the number of explanatory variables. The ordinal logistic regression technique was used to develop the above models. The regression coefficients were tested for significance at a level of 95%, which means that any variable with a \(p\)-value of less than 0.05 is considered to be statistically significant. Below, Tables 5-8 show the regression co-efficient and goodness of fit test results for models A, B, C and D, which were developed using a forward selection method and only included statistically significant variables at 95% confidence level. In the first model (Model A), a dataset including all 1141 interactions (with or without evasive action) was used as it was not feasible to estimate indicators for the moment of evasive action for the complete dataset. Therefore, to determine a value for these indicators for every interaction, the present analysis was constructed with the following goals:  
1. At first, a logistic regression model (model A) was developed using the entire dataset (N = 1141), taking the human judgement of severity as a dependent variable and objective measures that could be estimated for every interaction in the dataset (excluding the indicators estimated at the moment of evasive action) as an independent