Impacts of climate change on agro-climatic suitability of major food crops in Ghana

a single strong learner. This is achieved through sequentially building a series of smaller trees, where each tree tries to complement each other and correct for the residuals in the predictions made by all previous trees [53, 54]. The XGBoost algorithm develops the GBM approach fur- ther through using an ensemble of classification and regression trees (CARTs) to fit training data samples to targets [55, 56]. An independent binary tree decision rule structure is pro- duced for each CART and contains a continuous score on each leaf node, and for a given input, the output is the sum of the corresponding leaves’ scores [57, 58]. This is done in an additive way as the predictions are made from weak classifiers that constantly improve over the previous prediction error with higher weights at the next step to improve the scoring. The learning of the model in XGBoost is based on defining an objective function which describes the predictive accuracy of the model and regularization function describing the complexity [54, 55, 57] The XGBoost approach was developed by Chen and Guestrin [54] and has been widely rec- ognized as one of the best machine learning algorithms because it is fast, accurate and based on smaller models compared to similar family of models [55, 59]. It also has better results because it ameliorates the iterative optimization procedure inherent in traditional GBMs [54]. Specifically, for crop suitability modelling the XGBoost is able to provide a scaled four class model that is more representative than a binary suitable/unsuitable model in a computation-

ally efficient way for large scale spatial analysis, and since it reduces over-fitting with feature subsampling, it is more appropriate for model extrapolation under climate change. In recent machine learning performance studies, XGBoost has outperformed other algorithms [56, 60–62]. Parameter tuning for automatically determining the number of rounds, maximum tree depth and sigma was done using the caret package [63] while the XGBoost was imple- mented with the xgboost package [64] using the multi:softmax objective in R (version 3.5). The input data was randomly split into 70% for model fitting (training and validation) and the remaining 30% for independent model testing. 2.5 Identifying the contribution of variables to crop suitability We used the regularized gain to determine the contribution of each variable to suitability of each crop. The gain is the relative contribution of a variable to the model calculated by taking each variable’s contribution for each tree in the model. A higher value of this metric when compared to another variable implies it is more important for generating a prediction. If the difference between the full model (with all variables) and a model without a specific variable is small, it is assumed that the relative importance of this variable is low and vice versa. The con- tribution of each variable is then standardized between 0 (lowest importance) and 1 (highest importance) [65]. This approach is widely used in selection of variables that are important for predicted variables in machine learning. 2.6 Model evaluation

We used the confusion matrix to assess the accuracy of the modelled suitability classes relative to reference data that was set aside for model evaluation. The overall accuracy (OA), kappa coefficient, multi-class AUC and class specific metrics (sensitivity, specificity, positive predic- tion value, negative prediction value, precision, recall, F1-score, prevalence, detection rate, detection prevalence and balanced accuracy) were used as calculated from the confusion matrix. OA is the percentage that indicates the probability that a grid cell is modelled correctly by the model relative to the known reference data. The OA is calculated by dividing the sum of the entries that form the major diagonal (i.e., the number of correct classes) by the total num- ber of samples for each crop. The kappa coefficient (k) [66] measures the accuracy of the PLOS ONE Climate change and food crops suitability in Ghana PLOS ONE | https://doi.org/10.1371/journal.pone.0229881 June 29, 2020 6 / 21