# Accident Probability Prediction and Analysis of Bus Drivers Based on Occupational Characteristics
## 4 Data
### Data Filling
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **Variable** & **Mark** & **Description** & **Count** & **Proportion** & **Mean** & **Std.** \\ \hline \multirow{8}{*}{
\begin{tabular}{c} Trajectory information \\ \end{tabular} } & Average speed & Average speed & Continuous variables & - & - & 19.493 & 2.551 \\  & Speed dispersion & Speed dispersion & Continuous variables & - & - & 12.825 & 1.397 \\  & Acceleration & Acceleration & Continuous variables & - & - & 0.887 & 0.088 \\  & Acceleration dispersion & Acceleration & Continuous variables & - & - & 0.663 & 0.077 \\  & Azimuthal change & Azimuthal change & Continuous variables & - & - & 19.899 & 4.344 \\  & Maximum speed of station entry/exit & MSE & Continuous variables & - & - & 39.392 & 3.432 \\  & Average speed of station entry/exit & ASEE & Continuous variables & - & - & 21.655 & 2.046 \\  & Speed Dispersion of station entry/exit & SDEE & Continuous variables & - & - & 8.066 & 1.058 \\ \hline \multirow{8}{*}{Other} & \multirow{8}{*}{Weather} & \multirow{8}{*}{Weather} & 1 - Sunny & 56 & 5.08\% & \multirow{8}{*}{-} & \multirow{8}{*}{-} \\  & & 2 = Cloudy & 425 & 51.27\% & & \\ \cline{1-1}  & & 3 = Light rain & 310 & 28.13\% & & \\ \cline{1-1}  & & 4 = Moderate rain & 70 & 63.5\% & & \\ \cline{1-1}  & & 5 = Heavy rain & 45 & 4.08\% & & \\ \cline{1-1}  & & 6 = Rainstorm & 5 & 5.08\% & & \\ \cline{1-1}  & Rainfall & Rainfall & Continuous variables & - & - & 0.106 & 0.169 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._Figure 1: Distributions of continuous variables. Chained multiple interpolation usually performs well in dealing with complex, non-random, missing data, allowing for multiple variables to predict the missing values of a single variable. It also captures the relationship between the features, which is highly applicable to filling in non-random missing data [40; 41]. The MICEForest multiple interpolation method is based on the chained multiple interpolation method and employs an ensemble of decision trees (random forests) to improve missing data processing for machine learning applications [42]. The random nature of the results obtained from the random forests makes it more sensitive to missing values, more resistant to interference, and a more accurate interpolation method [43]. Meanwhile, compared with other multiple interpolations, MICEForest can insert missing classification and regression data without too many settings, leading to faster fill rates [44]. Therefore, in this paper, the MICEForest multiple interpolation method was used to fill the missing values of the dataset. The interpolation process is the following:  
1. For datasets containing missing values, Ori_Datase, randomly select some values within the missing attribute columns to fill the missing values in those columns. This process generates a randomly completed dataset called \"Rnd_dataset\" and forms the correlation coefficient matrix \"X_r.\"
2. Randomly choose a missing column from \"Rnd_dataset\", referred to as an incomplete attribute column A. Use the non-missing values of A to form the training set and the missing values of A as the test set. Construct a random forest model to predict the missing values of A. 3. Randomly select another attribute from the incomplete attributes, excluding A. Following the logic of the above filling missing value, iteratively impute the other incomplete attributes. This process creates the first iteration dataset \"Dataset_0\" and calculates the correlation coefficient matrix \"X_0\". 4. Use the convergence of correlation to determine whether \"X_r\" and \"X_0\" have converged. If they have not converged, return to step 2 and repeat the process, resulting in \"Dataset_1\" and correlation coefficient matrix \"X_1\". Once convergence is reached, the final dataset \"Dataset_0\" is obtained. 5. Repeat until n datasets are reached. In this paper, the MICEForest multiple imputation method generated five datasets, each statistically compared with the original dataset.