# Improvement of Wheat Grain Yield Prediction Model Performance Based on Stacking Technique
## 4 Discussion
In this study, the coupling of structural parameters (LAI) and spectral parameters (vegetation indices) of the crop effectively improved the accuracy of GY prediction at each growth stage, and the results of the \(t\)-test (Table 4) also fully demonstrated that the improvement of model effects at each growth stage was significant (\(p<0.05\)). This is because LAI is an important canopy structure information of crops and one of the important variables to determine the intensity of photosynthesis [4; 74]. The size of vegetation leaf area directly affects light interception, photosynthesis and transpiration efficiency of vegetation canopy, and is considered to be the most important factor affecting plant productivity [75]. The results are consistent with those reported by [PERSON] et al. [24] and [PERSON] et al. [76]. Among them, the most significant improvement in model accuracy was observed in the flagging stage (the relative value of R\({}^{2}\) increased by 22.5%) which is consistent with our statistical \(t\)-test (\(t=32.264\)). This is because the flagging stage is a critical period for the formation of wheat spike number, and this growth stage is mainly reflected in the rapid growth of leaf area and the consequent increase in photosynthetic efficiency, which contributes more to the accumulation of dry matter [77]. Our study demonstrated that canopy spectral saturation can be effectively overcome by coupling LAI and vegetation indices, and this study can provide a new method for accurate and rapid estimation of crop yield. The results of GY estimation at single growth stage indicated that there were significant differences in yield estimation at different fertility stages, which showed an increasing accuracy of prediction with the advancement of growth stage. This is because crop growth and development is a dynamic and continuous process, and changes in the growth state and environmental characteristics of the crop at each growth stage can lead to different morphological characteristics of the spectral curve, and thus the accuracy of the yield estimation models at different growth stages varies. Since each key stage of crop growth and development can have a significant impact on yield formation, it is important to find a method to combine information from multiple growth stages to improve the accuracy and robustness of the model. The objective of employing a stacking technique was to improve the prediction ability by combining data from multiple growth stages instead of using single growth stage data. When implementing a stacking approach, it is necessary to include self-sufficient, independent, and diverse base learners for analysis (Figure A3) [47]. The results showed that there was a strong correlation between the predicted results of different growth stages (correlation coefficients of R = 0.6-0.95), which was due to the overlap of information between adjacent fertility stages. ENET is used as a secondary model to perform the multicollinearity data analysis in the model when stacking multiple base learners due to its advantages of both ridge regression and lasso regression [63]. In this study, vegetation indices and LAI from four key growth stages of the crop were successfully combined to achieve higher accuracy in predicting grain yield than any single growth stage (Figures 5 and 6). In addition, the accuracy parameters (R\({}^{2}\) and RMSE) of the base learner fluctuated more and had a wider range than those of the ensemble approach, which also demonstrated the stability of the GY model constructed based on the Stacking technique. However, stacking techniques are sensitive to the timing of data collection at different growth stages. Due to the differences in developmental rates of different varieties, this may lead to the fact that different varieties may be at different growth stages at the same time.