## 3 Study 1. Knowledge-Driven Competence
### Competence Factors with a Machine Learning Method  
#### 3.3.1 Model  
In this section, our empirical research consists of three steps. First, to consolidate the framework of 10 competence-related traits and generate an accurate competence evaluation, a machine learning algorithm, XGBoost, was used to build the prediction model. Then, to make the results interpretable, SHAP was applied to rank the importance of the 10 traits. Finally, to further validate the results of the machine learning model, OLS regression was performed on the 10 traits and individual competence.  
(1) XGBoost  
In this section, we employed the XGBoost model to study whether our framework can be used to predict individual competence. XGBoost, a scalable machine learning system for tree boosting, has been widely proven to yield state-of-the-art results in many prediction tasks [95]. As essentially a gradient tree boosting algorithm, in XGBoost, a scalable end-to-end tree learning system is applied. The core idea of XGBoost is to continuously conduct feature splitting to train new regression tree functions \(f(x)\) and use them to fit the residual of the prediction in the previous round, as shown in Equations (1)-(4).  
\[\hat{y_{i}}^{(0)}=0 \tag{1}\]  
\[\hat{y_{i}}^{(1)}=f_{1}(x_{i})=\hat{y_{i}}^{(0)}+f_{1}(x_{i}) \tag{2}\]  
\[\hat{y_{i}}^{(2)}=f_{1}(x_{i})+f_{2}(x_{i})+=\hat{y_{i}}^{(1)}+f_{2}(x_{i})\dots \tag{3}\]  
\[\hat{y_{i}}^{(t)}=\sum_{k=1}^{t}f_{k}(x_{i})=\hat{y_{i}}^{(t-1)}+f_{t}(x_{i}) \tag{4}\]  
Here, \(\hat{y_{i}}^{(t)}\) is the prediction at training round \(t\). \(f_{t}(x_{i})\) is the new tree generated in round \(t\). In every round, the new function \(f_{t}(x_{i})\) should be the one that minimizes the objective in Equation (5).  
\[Obj^{(t)}=\sum_{i=1}^{n}l\left(y_{i}\,\ \hat{y_{i}}^{(t-1)}+f_{t}(x_{i}) \right)+\Omega(f_{t})+constant \tag{5}\]  
\(l\) denotes the loss function, and \(\Omega(f_{t})\) is the regularizer that penalizes the complexity of the model. Finally, the prediction \(\hat{y_{i}}\) is the summation of the predicted values of all trees, as shown in Equation (6).  
\[\hat{y_{i}}=\varnothing(x_{i})=\sum_{k=1}^{K}f_{k}(x_{i}) \tag{6}\]  
By explicitly adding a regularizer to the model, XGBoost excels at avoiding overfitting and thus improving the generalizability of the model. In addition, a tree learning algorithm and justified weighted quantile sketch procedure are applied; thus, this model also excels at handling sparse data and achieving efficient calculation.  
In our study, we trained and tested the model with video clips from the CH-CMD, which contains 2374 samples in total. We randomly selected 80% of the video clips as train  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Variable** & **Description** & **Mean** & **SD** & **Min** & **Max** & **API Algorithm** \\ \hline \multicolumn{8}{c}{**Control Variable**} \\ \hline \multirow{2}{*}{Gender} & Female influencers are labeled as 0, male influencers are labeled as 1. & 0.096 & 0.276 & 0 & 1 & Face++ \\ \hline \multicolumn{8}{c}{Note: OpenFace 2.0 is a framework to implement a modern facial behavior analysis algorithm. Librosa is a Python package for audio analysis. Face++ is a platform offering computer vision technologies such as face detection, face search, face landmarks, and face masks.} \\ \end{tabular}
\end{table}
Table 3: _Cont._ing data and the remaining video clips as test data. We set the learning rate to 0.01 and the number of trees to 100. Finally, in the task of predicting perceived individual competence, a mean square error (MSE) of 7.335 \(\times\)\(10^{-6}\) and a root mean square error (RMSE) of 0.002708 were obtained using this model. These results indicate that our competence evaluation framework contains valid information about perceived competence.