# Pavement Distress Initiation Prediction by Time-Lag Analysis and Logistic Regression
## 4 Results and Discussion
### Correlation Analysis  
The time-lag phenomenon has been extracted from the relationship between pavement distress initiation and meteorological data in the above analysis, but the effect of the time delay in predicting distress initiation should be further discussed. Therefore, the binary Bayesian logistic regression model should be established to assess the contribution of the time delay effect by considering time lag in weather variables' value. Based on the preliminary temporal correlation analysis results, the weather variables considered the time delay effect by setting a time lag in variables' value calcula  
Figure 5: WTLCC charts between the cumulative number of distress initiations (No_DIS_INI) and meteorological variables. (**a**) WTLCC between No_DIS_INI and daily maximum temperature; (**b**) WTLCC between No_DIS_INI and daily minimum temperature; (**c**) WTLCC between No_DIS_INI and daily average temperature; (**d**) WTLCC between No_DIS_INI and daily total precipitation; (**e**) WTLCC between No_DIS_INI and relative humidity. tion. The time lags of maximum temperature (MAX_TEMP_LAG), minimum temperature (MIN_TEMP_LAG), the daily average temperature (AVG_TEMP_LAG), daily total precipitation (RH_LAG), and relative humidity (PRCP_LAG) were set as zero, 9 days, 9 days, 2 days, and zero, respectively. Specifically, the value of the weather variables with time-lag t means the meteorological variable's value t days ago. For example, the precipitation variable on 16 May was 29.8 mm, and the precipitation variable with a 2-day time lag was 10.7 mm on 14 May. Therefore, the rest of the weather variables with time lag can be obtained with the same approach. Figure 6 presents the correlation coefficients of seven numerical variables with the pavement distress initiation. The red and blue boxes in the correlation coefficients matrix indicate that the counterpart variables have positive and negative correlations, respectively. The color depth indicates the level of positive and negative correlations. Three light blue boxes in the cumulative number of distress initiations column illustrate that maximum temperature, minimum temperature, and the daily average temperature during the study period have negative correlations with pavement distress initiation, which means the probability of distress occurrence would decrease if the temperature-dependent numerical variables go up. Significantly, the three deep red boxes illustrate that maximum temperature, minimum temperature, and the daily average temperature have remarkable positive correlations, which is easy to understand provided that daily average temperature was calculated with maximum and minimum temperature. So, to reduce the effect of highly relevant variables in regression modeling, the daily average temperature was considered in the modeling, and the maximum and minimum temperatures were excluded. Moreover, two light red boxes in the cumulative number of distresses column under the temperature boxes illustrate that daily total precipitation and relative humidity negatively correlate with distress initiation. It can be described as higher precipitation values, and relative humidity leads to a higher possibility of distress initiation, which means more moisture content in the atmosphere might cause pavement surface conditions to deteriorate. Furthermore, the distance between the current coordinate and the nearest intersection negatively correlates with distress initiation via a light blue box. Significantly, the box between the distance from the current coordinate to the nearest intersection center (DIS_NEAR_INT) column and the cumulative number of distresses within 50 m of the current coordinate (No_ADJ_DIS) column is light blue, illustrating that distance increases between the current coordinate and the nearest intersection would reduce the cumulative number of pavement distresses.