## 4 Methodology  
We select the XGBoost model to predict the transfer ridership at bus-metro-transfer stations and rank the relative importance of the independent variables. The nonlinear relationship between the bus-metro-transfer ridership and important independent variables as well as the threshold adjustment utility is explained by generating a partial dependence plot. XGBoost was an extensible tree-enhancement system and a kind of boosting algorithm [69]. The core idea of boosting the algorithm was to add many base models together, to form a strong classifier. XGBoost combined many CART trees. When data cannot be well fit by one tree, multiple CART trees were used to approach it, instead [87]. The advantage of the XGBoost model is adding a regularization term and second-order Taylor expansion, to avoid over-fitting in the high-precision calculation. The model prediction output of XGBoost is shown in Equation (1):  
\[\hat{y}=\sum_{k=1}^{K}f_{k}(x_{i}) \tag{1}\]  
where \(\hat{y}\) is the sum of the prediction results of \(k\) samples, \(f_{k}(x_{i})\) is the prediction result of the \(k\)-th sample. The loss function is shown in Equation (2):  
\[\mathcal{L}=\sum_{i=1}^{N}l(y_{i},\hat{y}_{i})+\sum_{k}\Omega(k) \tag{2}\]  
where \(l\) is a common loss function used to measure the difference between the actual value of each sample \(y_{i}\), and the predicted value of each sample \(\hat{y}\), \(\Omega(k)\) is a regularization term, which describes the complexity of the tree. The complexity of decision tree \(k\) can be defined as Equation (3):  
\[\Omega(k)=\gamma\cdot T+\frac{1}{2}\lambda\sum_{j=1}^{T}\omega_{j}^{2} \tag{3}\]where \(T\) is the number of leaf nodes in the decision tree, \(\omega_{j}\) is the score of each leaf, and \(\gamma\) and \(\lambda\) are penalty parameters. \(\mathcal{L}^{(t)}\) is the \(t\)-th round objective function, obtained through continuous iterative optimization, which can be described as Equation (4):  
\[\mathcal{L}^{(t)}=\sum_{i=1}^{n}l\Big{(}y_{i},\hat{y}_{i}{}^{(t-1)}+q_{t}(x_{i} )\Big{)}+\gamma\cdot T+\frac{1}{2}\lambda\sum_{j=1}^{T}\omega_{j}^{2} \tag{4}\]  
where \(q_{t}\) is the addition example of the \(t\)-th iteration, carry out the second-order Taylor expansion at \(\hat{y}_{i}{}^{(t-1)}\) to, continuously, approximate the value of the objective function, as shown in Equation (5):  
\[\mathcal{L}^{(t)}=\sum_{i=1}^{n}\biggl{[}l\left(y_{i},\hat{y}_{i}{}^{(t-1)}+g_ {i}q_{t}(x_{i})+\frac{1}{2}h_{i}q_{t}^{2}(x_{i})\right)\biggr{]}+\gamma\cdot T +\frac{1}{2}\lambda\sum_{j=1}^{T}\omega_{j}^{2} \tag{5}\]  
where \(g_{i}=\partial_{\hat{y}_{i}{}^{(t-1)}}l\left(y_{i},\hat{y}_{i}{}^{(t-1)} \right)\), \(h_{i}=\partial_{\hat{y}_{i}{}^{(t-1)}}^{2}l\left(y_{i},\hat{y}_{i}{}^{(t-1)} \right)\). Since we only need to consider the variables in optimization, the constant term is removed, and all samples will, eventually, fall on a leaf node, no matter which way they go. Therefore, the combined formula can be written as shown in Equation (6):  
\[\mathcal{L}^{(t)}=\sum_{j=1}^{T}\left[\left(\sum_{iel_{j}}g_{i}\right)\omega_{ j}+\frac{1}{2}\left(\sum_{iel_{j}}h_{i}+\lambda\right)\omega_{j}^{2}\right]+ \gamma\cdot T \tag{6}\]  
where \(I_{j}=\left\{i|q(x_{i})=j\right\}\), represents the sample set falling on the \(j\)-th leaf node. The selection of features and the correlation between features and prediction targets largely determines the prediction accuracy of this study. Due to the complexity of influencing factors, such as bus-metro connection characteristics, land-use attributes, network attributes of metro stations, and demographic factors, with the existing single-machine-learning model, it is difficult to solve the problem of multicollinearity processing of multi-source data. The high correlation between features can, also, reduce the robustness of the model, resulting in over-fitting in training. It is necessary to reprocess the multi-source transfer data to obtain the features with strong correlation with the prediction target.