# Pavement Distress Initiation Prediction by Time-Lag Analysis and Logistic Regression
## 4 Results and Discussion
### Logistic Regression Analysis Results
On the contrary, in the logistic regression model, the significance of the grades of the upstream and downstream adjacent road sections was not significant, possibly because this variable is an indirect response to the traffic volume of the road section, which does not correspond to the actual traffic volume and, therefore, does not show significance in this study. The logistic regression model reflects the degree of influence of the variable parameters on the predicted values by means of probability ratios. For example, the cumulative number of distresses within 50 m of the current coordinate (No_ADJ_DIS) parameter shows a highly significant coefficient equal to 0.1591, which indicates that the probability ratio of pavement distresses' occurrence will increase by 1.172 (equals to e to the 0.1591) times when the number of historical distresses increases by one. All significant variables in both models showed the same trend and differed only in their values, showing the correctness of the prediction models. Among the weather factors, the coefficients of daily average temperature and relative humidity are similar in both models, while the coefficient of daily precipitation in model 1 is 0.046 greater than that of model 2, which indicates that the consideration of time lag on daily precipitation will have a greater impact on the prediction accuracy of distress generation. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & \multicolumn{3}{c}{**The Model Contains Weather Variables with**} & \multicolumn{3}{c}{**The Model Contains Weather Variables without**} \\  & \multicolumn{3}{c}{**Time Lag (Model 1)**} & \multicolumn{3}{c}{**Time Lag (Model 2)**} \\ \cline{2-7}  & **Estimate** & **Std.** & **95\% BCI** & **Estimate** & **Std.** & **95\% BCI** \\ \hline Intercept & \(-1.219\) & 0.545 & \([-2.287,-0.151]\) & \(-0.717\) & 0.544 & \([-1.783,0.348]\) \\ UP\_RD\_GRADE & 0.093 & 0.096 & \([-0.096,0.282]\) & \(-0.022\) & 0.092 & \([-0.203,0.159]\) \\ DOWN\_RD\_GRADE & \(-0.050\) & 0.095 & \([-0.236,0.137]\) & \(-0.0638\) & 0.092 & \([-0.244,0.116]\) \\ AVG\_TEMP\_LAG & \(-0.090\) *** & 0.010 & \([-0.110,-0.069]\) & - & - & - \\ PRCP\_LAG & 0.046 *** & 0.010 & \([0.025,0.064]\) & - & - & - \\ RH\_LAG & 0.027 *** & 0.004 & \([0.019,0.035]\) & - & - & - \\ AVG\_TEMP & - & - & - & \(-0.093\) *** & 0.011 & \([-0.114,-0.072]\) \\ PRCP & - & - & - & 0.023 * & 0.011 & \([0.001,0.046]\) \\ RH & - & - & - & 0.026 *** & 0.005 & \([0.017,0.035]\) \\ DIS\_NEAR\_INT & \(-0.001\) *** & 0.000 & \([-0.002,0.000]\) & \(-0.0009\) * & 0.000 & \([-0.002,0.000]\) \\ No\_ADJ\_DIS & 0.1591 *** & 0.023 & \([0.115,0.203]\) & 0.1994 *** & 0.023 & \([0.155,0.244]\) \\ \hline \multicolumn{7}{c}{**Model Performance**} \\ \hline AIC & & 1335.703 & & 1371.775 & \\ BIC & & 1375.964 & & 1412.036 & \\ Train AUC & & 0.759 & & 0.748 & \\ Test AUC & & 0.761 & & 0.749 & \\ \hline \hline \end{tabular}  
***: \(p\)-value \(<0.001\). *: \(p\)-value \(<0.05\). BCI: Bayesian Confidence Interval (95%).  
\end{table} 
Table 3: Results of Bayesian Logistic Regression Models.