## 5 Modelling of Lane-Changing Behaviours (LCB)
### Development of LCB Model  
Logit and probit regression models have been widely used in various traffic analyses to investigate and evaluate accidents, driver behaviour, and related factors [44; 45; 46]. In the study, these models were applied to determine drivers' lane-changing behaviour. In the \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \begin{tabular}{c} **Variable** \\ **Name** \\ \end{tabular} & \multirow{2}{*}{**Scenario No**} & \multirow{2}{*}{**Lighting Colour**} & \multirow{2}{*}{**Observation**} & \multirow{2}{*}{**Min.**} & \multirow{2}{*}{**Max.**} & \multirow{2}{*}{**Mean Value**} & \multirow{2}{*}{\
\begin{tabular}{c} **Std.** \\ **Deviation** \\ \end{tabular} } \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Speed \\ (km/h) \\ \end{tabular} } & S-1 & Blue digit & 125 & 44.5 & 151.2 & 27.4 & 7.8 \\ \cline{2-7}  & S-2 & Red digit & 125 & 23.4 & 153.8 & 27.1 & 9.8 \\ \cline{2-7}  & & Green digit & 125 & 20.8 & 152.8 & 29.8 & 8.6 \\ \cline{2-7}  & & Red Wall Light & 125 & 24.7 & 154.6 & 38.0 & 9.1 \\ \cline{2-7}  & S-3 & Red Wall Light & 125 & 22.1 & 152.9 & 25.5 & 10.9 \\ \cline{2-7}  & Green Light & 125 & 41.8 & 155.6 & 28.1 & 8.9 \\ \hline \multicolumn{7}{c}{Age (year)} & 125 & 18 & 76 & 38.1 & 11.0 \\ \hline \multicolumn{7}{c}{Driver Experience (year)} & 125 & 1 & 37 & 10.3 & 9.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Descriptive statistics of numerical variables. Figure 9: Input variables in graphic form. conducted analysis, the dependent variable in both logit and probit regression models could only take two values, making it possible to explore the limitations of these models when compared to a linear probability model (LPM). Both the logit and probit models share similar characteristics, with only small differences between them. The logit model uses the odds ratio, while the probit model applies the Gaussian (normal distribution) function. To determine which model best describes the relationship between LCB and the given parameters, the log-likelihood information and [PERSON]'s R\({}^{2}\) values were used in the analysis. In a well-fitting model, both of these values should be high [43; 47]. A comparison analysis between the logit and probit models was made to assess which better explains the relationship between LCB and the influencing parameters (see Table 8). As shown in Table 8, the probit model outperformed the logit model, with higher log-likelihood information and [PERSON]'s R\({}^{2}\) values, indicating that it better describes the suggested model for each scenario. Therefore, the probit model was used to model lane-changing behaviours in all scenarios. In the developed model given in Table 9, the variance inflation factor (VIF) was calculated for each covariate to check for potential multicollinearity and model specification errors. The results showed that the maximum VIF (S-1 = 3.19; S-2 = 3.21; S-3 = 3.10) was below the threshold of 10, indicating that the model had no multicollinearity issues [42; 48]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scenario No** & **Parameter** & **Logit Model** & **Probit Model** \\ \hline \multirow{4}{*}{S\(-\)1} & \(p>\) Likelihood Ratio & 0.091 ** & 0.090 ** \\  & Log– Likelihood Full Model & \(-\)74.1 & \(-\)72.5 ** \\  & [PERSON]’s R\({}^{2}\) & 0.65 & 0.66 ** \\ \hline \multirow{4}{*}{S\(-\)2} & \(p>\) Likelihood Ratio & 0.084 ** & 0.081 ** \\  & Log– Likelihood Full Model & \(-\)196.7 & \(-\)185.2 ** \\  & [PERSON]’s R\({}^{2}\) & 0.72 & 0.74 ** \\ \hline \multirow{4}{*}{S\(-\)3} & \(p>\) Likelihood Ratio & 0.000 * & 0.000 * \\  & Log– Likelihood Full Model & \(-\)222.055 & \(-\)221.969 ** \\ \cline{1-1}  & [PERSON]’s R\({}^{2}\) & 0.79 & 0.80 ** \\ \hline \hline \end{tabular} Note. * Shows statistically more significant than other, ** Significant at 0.01 level, * Significant at 0.01 level.  
\end{table} 
Table 8: Comparison of logit and probit models for the proposed LCB models.