# Improvement of Wheat Grain Yield Prediction Model Performance Based on Stacking Technique
## 3 Results
### Comparative Analysis of Grain Yield Prediction Accuracy from Multiple Growth Stages  
To evaluate the performance of the stacking method, the ENET algorithm was used as a secondary model to construct GY prediction model by integrating the prediction results of the four growth stages with and without coupled LAI in two cases, respectively. The accuracy of GY prediction results obtained by combining four of the base learners were presented in Figure 6.  
The GY prediction model based on multiple growth stages was constructed using only the vegetation indices as the input factors for the model. The average prediction accuracy of the integrated model was R\({}^{2}\) = 0.67, RMSE = 0.85 t ha\({}^{-1}\). Overall, the GY prediction accuracy of the integrated multiple growth stages had been improved to varying degrees compared with the four single growth stages. Compared with the prediction accuracy of GY at the jointing, flagging, anthesis, and grain filling stages, the average R\({}^{2}\) of the integrated model increased by 235%, 67.5%, 19.6% and 11.7%, and the average RMSE decreased by 36.1%, 28%, 19.8%, and 9.6%, respectively.  
The vegetation indices coupled with LAI were used as the input factors of the model to construct a GY prediction model by integrating multiple growth stages. The results showed that the prediction accuracy of the integrated model was R\({}^{2}\) = 0.74, RMSE = 0.81 t ha\({}^{-1}\). Overall, after integrating the multiple growth stages, the prediction accuracy of GY had been improved to varying degrees. Compared with the jointing, flagging, anthesis and grain filling stages, the average R\({}^{2}\) values of the integrated model increased by 236%, 51%, 27.6% and 12.1%, and the average RMSE decreased by 38.2%, 26.4%, 20.6%, and  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Growth Stage** & \(t\) & \(p\)**Value** \\ \hline Jointing & 12.135 & 0.000 \\ Flagging & 32.264 & 0.000 \\ Anthesis & 9.106 & 0.000 \\ Grain filling & 26.525 & 0.000 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Results from the paired sample \(t\)-test.  
8%, respectively. Based on the analysis of the above research results, the vegetation indices coupled with LAI were used as the model input factors, and based on the stacking technology, a GY prediction model integrating the four growth stages was constructed, yielding highest verification accuracy (R\({}^{2}\) = 0.74, RMSE = 0.81 t ha\({}^{-1}\)).  
To further verify whether the improvement in GY prediction accuracy by integrating information from multiple growth stages is significant, paired samples _t_-tests were used to assess whether there is a statistical difference in the validation R\({}^{2}\) between the integrated model and the single-growth stage model under two cases of vegetation indices with and without coupled LAI, respectively. The results were listed in Table 5.  
The results showed that the integrated model outperformed the other base models with or without LAI, and the \(p\) values were less than 0.05 indicating that the accuracy improvement obtained by the integrated model was statistically significant. This further demonstrated the effectiveness of the stacking technique proposed in this paper for GY prediction. Among them, the accuracy of the jointing stage was improved most evidently, and the \(t\) value was the highest (_t_ = 51.153 and \(t\) = 60.18, respectively), consistent with the above results. Moreover, when the vegetation indices coupled with LAI were used as the input factors of the model, the prediction accuracy of the integrated model improved more evidently, and GY prediction effect was better.