## 4 Discussion
### Benefit of Variable Importance of Random Forest  
In this study, the variable importance in RF analysis was used to determine important predictor variables for developing a better estimation model and for improving prediction accuracy. This method has been used to determine the important variable of RF regression in predicting plant density and vegetation biomass using vegetation indices and multi-spectral instruments [22; 59; 60]. The newly developed model based on this method, the 10 VarImp-RF model, showed a better prediction value (\(r^{2}\) 0.68 and RMSE 1.72 plants m\({}^{-2}\)) than the other regression models (Figure 9). The accuracy of the 10 VarImp-RF model was more robust compared to a previous study by [PERSON] et al. [22], who also predicted soybean plant density using RF regression treating multiple vegetation indices derived from an RGB UAV imagery as explanatory variables (RMSE: 3.91-7.47 plants m\({}^{-2}\)). Thus, the 10 VarImp-RF model result may indicate that the selection of predictor variables based on variable importance would be an effective approach. Although the variable selection was reported to generate some bias in the classification task of RF, the potential of causing biased results in regression tasks has not been discussed [61]. The results demonstrated that variable selection might also be an essential process in enhancing the prediction accuracy of the RF model for regression tasks. The variable importance of the RF regression model indicated that the NIR bands at 30 and 40 DAS were the first and fifth most important variables, respectively (Figure 8). Near-infrared reflectance is sensitive to changes in vegetation structure and leaf area index [29], which was also influential in predicting plant density. The normalized difference vegetation index at 20, 30, and 40 DAS was also within the ten most important variables. Overall, PlanetScope reflectance and NDVI values from the later growth stage that were close to flowering time, which was approximately 30-40 DAS, played relatively important roles in predicting plant density compared to the early growing stage. Red, green, and blue bands did not appear in the fifth most important variables. The variable importance of RF regression further indicated that precipitation before sowing dates affected the plant density of soybean, probably because water availability is the main factor affecting the vegetation growth of plants [30]. Rainfall events could provide favorable conditions for both seedling emergence and subsequent leaf expansion. On the other hand, excessive soil moisture and submergence due to the heavy rain is reported to result in low emergence rate of seedling [5] and to retard leaf expansion in the early vegetative stage [31]. Therefore, rainfall data may have nonlinear effects on either leaf area or plant density. The significant errors in the PLS regression models for Field 9 (Figure 6d-f) also indicate the importance of nonlinear relationships between precipitation and plant density, because PLS regression is theoretically based on a linear assumption between the variables. Furthermore, a suitable temperature in the early days of emergence is also needed for seedlings to the emergence and represents the importance of cumulative temperature at 10 DAS in the RF model. High temperatures and low precipitation rates after sowing could promote drought, which could also decrease or delay emergence and plant growth [62]. The soybean growth rate in the juvenile stage after emergence responds strongly to temperature and water stress conditions [63]. Thus, climate data might have contributed to increasing the RF model's accuracy (Table 3). However, note that climate data had a 1 km\({}^{2}\) spatial resolution, resulting in almost regionally identical values across fields; thus, it could not contribute to increasing the prediction accuracy in terms of within-field spatial variability of plant density.