# Improvement of Wheat Grain Yield Prediction Model Performance Based on Stacking Technique
## 3 Results
### Elastic Network for Grain Yield Prediction  
Based on the ENET, the vegetation indices and the vegetation indices coupled LAI were used as the input factors for the model to construct GY prediction models for four growth stages, respectively. Based on the prediction results, the box-plot of GY prediction accuracy for each growth stage was drawn with or without LAI, as shown in Figure 5.  
Only 15 vegetation indices were used as the input features of the model to construct the GY prediction model for each growth period. The results showed that GY prediction accuracy at the jointing stage was R\({}^{2}\) = 0.20, RMSE = 1.33 t ha\({}^{-1}\); the GY prediction accuracy at the flagging stage was R\({}^{2}\) = 0.40, RMSE = 1.18 t ha\({}^{-1}\); the GY prediction accuracy at the anthesis stage was R\({}^{2}\) = 0.56, RMSE = 1.06 t ha\({}^{-1}\); the GY prediction accuracy during the grain filling period was R\({}^{2}\) = 0.60, RMSE = 0.94 t ha\({}^{-1}\). The above results show that the prediction accuracy R\({}^{2}\) of the GY prediction model based on the vegetation indices increased with the growth period and that the RMSE decreased with the growth of winter wheat, indicating that GY prediction ability for winter wheat increased with the growth period and reached the best prediction effect at the grain filling stage.  
To study the influence of LAI on the accuracy of winter wheat GY prediction model, 15 vegetation indices of the four growth periods coupled with LAI of the same growth period were used as input factors for the model to construct a single-growth-period GY prediction model. The results showed that R\({}^{2}\) = 0.22, RMSE = 1.31 t ha\({}^{-1}\) at the jointing  
Figure 4: Correlation between grain yield and indices of each growth stage.  
Figure 5: The statistical distributions of the prediction accuracy of each growth stage for grain yield prediction in the test phases; (**a**) distributions of R\({}^{2}\) at each individual stage; (**b**) distributions of RMSE at the each individual stage.  
stage, R\({}^{2}\) = 0.49, RMSE = 1.1 t ha\({}^{-1}\) at the flagging stage, R\({}^{2}\) = 0.58, RMSE = 1.02 t ha\({}^{-1}\) at the anthesis stage, and R\({}^{2}\) = 0.66, RMSE = 0.88 t ha\({}^{-1}\) at the grain filling stage. Overall, the prediction accuracy of GY of winter wheat gradually increased with the growth period, and the prediction accuracy of the model at the grain filling stage was the highest.  
The results showed that the 15 vegetation indices could be coupled with LAI to construct a GY prediction model. During the jointing, flagging, anthesis, and grain filling stages, the average R\({}^{2}\) of GY prediction model increased by 10%, 22.5%, 3.6% and 10%, the average RMSE were reduced by 1.5%, 6.7%, 3.8%, and 6.4%, respectively. A comparative analysis of the above results showed that GY prediction accuracy of each growth period had been improved after coupling the vegetation indices with LAI. Among them, the GY prediction accuracy of the flagging stage had improved the most.  
To further verify the performance of GY prediction by coupling LAI with the vegetation indices, a paired \(t\)-test was used to evaluate whether there was a significant difference in the impact of vegetation indices on GY prediction accuracy when coupling with LAI, as listed in Table 4.  
The results showed that the \(p\)-values for all four growth stages were less than 0.05, indicating that the vegetation indices coupled with LAI were used to construct GY prediction models with statistically significant improvement in prediction accuracy. The \(T\) value of the flagging stage was the highest (\(t\) = 32.264), and the accuracy was improved most evidently.  
As shown in Figure 10, the Pearson's correlations between the GY predictions for the four individual growth stages were high (r = 0.6-0.95). By contrast, the density curves of the grain yield predictions were slightly different from each other. Moreover, the base learners differed significantly in the distribution interval of the prediction accuracy.