# Multi-Output Based Hybrid Integrated Models for Student Performance Prediction
## 3 Materials and Methods
### Model Comparison
#### 3.7.1 Comparison of Classification Models  
Table 6 and Figure 7 depict the performance evaluation of three different imputation methods when predicting scores during the forecast period, wherein the Xgboost model achieved an accuracy of 78.37% under the mean imputation method, which was 2-5% higher than other models. Furthermore, the recall and F1 score of the Xgboost model was superior to all other models, while its precision was lower than the best model by 2%. Combining the information presented in the tables and figures, the Xgboost model under the mean imputation method demonstrated the most favorable performance in predicting scores during the forecast period. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Parameter Settings** & **Accuracy/\(MSE\_a\)** \\ \hline m\_xgboost(midterm exam) & learning\_rate=0.1,max\_depth=2, & 0.7837 \\  & n\_estimators=100,max\_delta\_step=0.2 & \\ \hline
0\_xgboost(midterm exam) & learning\_rate=0.9,n\_estimators=50, & 0.7567 \\  & min\_child\_weight=2,max\_depth=2 & \\ \hline
0\_gdbt(midterm exam) & random\_state=40,learning\_rate=0.55,n\_estimators=100 & 0.7567 \\ \hline m\_xgboost(final exam) & max\_depth=3,learning\_rate=0.19,n\_estimators=100, & 0.7837 \\  & min\_child\_weight=1,max\_delta\_step=0.4 & \\ \hline r\_xgboost(final exam) & learning\_rate=0.70,n\_estimators=100, & 0.7567 \\  & min\_child\_weight=1,max\_delta\_step=0.2 & \\ \hline
0\_xgboost(final exam) & learning\_rate=0.90,max\_depth=8, & \\  & min\_child\_weight=1,max\_delta\_step=0.5 & \\ \hline m\_gdbt(process grade) & random\_state=40,learning\_rate=0.01,subsample=0.2 & 16.7699 \\ \hline m\_randomforests(process grade) & random\_state=40,max\_depth=2,min\_samples\_leaf=10 & 17.1784 \\ \hline r\_gdbt(process grade) & random\_state=40,learning\_rate=0.01,subsample=0.2 & 17.7929 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Model parameter. As shown in Table 8 and Figure 9, the Xgboost model under the mean imputation method in Method 2 outperformed other models by 2-10% in terms of accuracy and was approximately 3% higher in accuracy than the best-performing Lightgbm model in Method 1. Moreover, it demonstrated superior performance in other evaluation indicators compared to the Lightgbm model in Method 1. Based on the information presented in the tables and figures, selecting the predictive model in Method 2 generally yields better results than the predictive model in Method 1. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **Accuracy** & **Precision** & **Recall** & **F1** \\ \hline r\_kgb & 0.7567 & 0.6875 & 0.7333 & 0.7096 \\ r\_gdbt & 0.7567 & 0.7142 & 0.6666 & 0.6896 \\ r\_adboost & 0.7567 & 0.7142 & 0.6666 & 0.6896 \\ m\_xgboost & 0.7297 & 0.6470 & 0.7333 & 0.6875 \\ m\_gdbt & 0.7297 & 0.6666 & 0.6666 & 0.6666 \\ r\_xgboost & 0.7297 & 0.6923 & 0.6 & 0.6428 \\
0\_xgboost & 0.7027 & 0.6428 & 0.6 & 0.6206 \\
0\_gdbt & 0.7027 & 0.6666 & 0.5333 & 0.5925 \\ m\_randomforests & 0.7027 & 0.6428 & 0.6 & 0.6206 \\ m\_jbg & 0.7027 & 0.6111 & 0.7333 & 0.6666 \\ m\_adboost & 0.7027 & 0.6428 & 0.6 & 0.6206 \\
0\_randomforests & 0.6756 & 0.6 & 0.6 & 0.6 \\
0\_jbg & 0.6756 & 0.6 & 0.6 & 0.6 \\ r\_randomforests & 0.6756 & 0.6 & 0.6 & 0.6 \\
0\_adboost & 0.6486 & 0.5625 & 0.6 & 0.5806 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Evaluation indicators of final performance prediction based on method \(1\).