# A Geographically Weighted Random Forest Approach to Predict Corn Yield in the US Corn Belt
## 1 Introduction
VIs such as the normalized difference vegetation index (NDVI), enhanced vegetation index (EVI), soil-adjusted vegetation index (SAVI), green chlorophyll index (GCI), and normalized difference water index (NDWI) are generally used to characterize vegetation conditions and have recently been used to study crop yield [11; 13; 31; 37]. NDVI and EVI have been calculated and used as independent variables in combination with several other variables such as climate and soil data to predict crop yield in different areas [11; 31]. Another factor recently used for estimating crop yield is primary productivity [9], which can be defined as the amount of carbon taken by plants to create new biomass [45]. There are a variety of machine learning models that can be used to predict crop yield [16]. These input parameters of machine learning models include climate data (temperature, precipitation, evapotranspiration, and vapor pressure), soil conditions (soil organic carbon, soil moisture, and soil temperature), and management factors (planting pattern, sowing, and harvesting dates) [25]. [PERSON], [PERSON], [PERSON] and [PERSON] [11] developed a spatio-temporal neural network model that uses remote sensing, soil, and climate data to predict winter wheat yield. They also compared their results with those of other benchmark models such as support vector regression, and the results show that spatio-temporal models can improve winter wheat yield prediction by 2.61% in terms of mean absolute percentage error (MAPE). [PERSON], [PERSON], [PERSON] and [PERSON] [31] used Bayesian neural networks (BNN) to predict corn yield in the US Corn Belt and achieved a coefficient of determination (R\({}^{2}\)) of 0.77. The results of BNN were compared with those from other models, and their results show that BNN can reduce the overall error by 6 to 23%. [PERSON], [PERSON] and [PERSON] [10] used machine learning ensembles to predict corn yield in three US states: Illinois, Iowa, and Indiana. A wide range of predictors were used to carry out this study, and their method can improve corn yield prediction by approximately 5%. Another study based on the coupling of physical models with machine learning models reported that the inclusion of machine learning algorithms can improve the accuracy of the models [38]. [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] [40] used convolution neural networks (CNN) to predict county-level soybean yield (R\({}^{2}\) = 0.77). Their CNN model achieved a very high accuracy (R\({}^{2}\) = 0.77). Previous studies have used several different predictors at different spatio-temporal scales to predict corn yield [11; 13; 27; 31; 33; 46]. These studies also employed different machine learning models that have improved performance when compared with other models in terms of R\({}^{2}\), mean squared error (MSE), and mean absolute error (MAE) [25; 46]. The improved results can be attributed to different factors such as the complexity of models, the number of independent variables, and the scale of study [28; 32]. However, as mentioned earlier, it can be difficult to collect data for a large number of features in a large study area. Moreover, using a large number of predictors in machine learning models can possibly increase uncertainty as machine learning models are prone to overfitting issues [38; 39]. In this context, selecting a set of key features is important in constructing crop yield prediction models [47]. Relevant research needs to be conducted to derive the best set of predictors for the machine learning models for crop yield prediction. Additionally, crop yield prediction has a spatial nature, and spatial factors play a significant role in crop yield modeling [48]. However, the spatial variations in crop yield have rarely been considered in previous studies. Addressing spatial problems with non-spatial methods can introduce uncertainty in the results. The models trained without considering geographic locations of samples sometimes cannot capture the local effects [6; 23; 28; 31; 37].