Effect of climate and geography on worldwide fine resolution economic activity

with collinearities [24], correlated variables are not eliminated. Instead, by retaining them we allow for multiple (correlated) predictors to emerge when assessing the variable ranking. If two or more highly correlated variables turn out to be the most important, this result will sig- nal the relevance of that group of predictors. Indeed, if we were to remove collinearities a pri- ori we would not be able to identify recurrent important variables (this was tested by eliminating highly correlated variables and retaining only one amongst them). Predictors are primarily selected and ranked using the standard Mean Absolute Error (MAE). Root-Mean- Square Difference (RMSD) and linear correlation were also computed, and results are essen- tially the same as for MAE. Variable ranking This procedure consists in the ordering of the complete set of all the 121 variables, and it is based on a forward step-wise methodology which retains a variable at the time, starting with no variables and recursively adding the variable which yield the largest MAE reduction of the GCP-PC [25]. A k-fold (with k equal to 5) cross validation procedure is performed to estimate the MAE prediction statistic. The k-fold validation is commonly used to test the performance of a prediction model, particularly when there are not independent data for validation [25]. Essentially, a sample is divided into k equally populated randomly selected sub-samples. In turn, (k-1) sub-sample(s) is/are used for the training and the remaining sub-sample is used for the prediction. The most typical values of k are 5 or 10.

Four samples are considered: 1. All grid points (namely most of the world); 2. Grid points in the top (or upper) third (or tercile) of the GCP-PC distribution; 3. Grid points in the middle tercile of the GCP-PC distribution; 4. Grid points in the bottom (or lower) tercile of the GCP-PC distribution. As well as identifying the explanatory variables for regions with different productivity (with samples 2, 3 and 4), these samples also allow to reduce the potential geographical correlation of GCP, in addition to the use of random sampling applied to the k-fold validation. Moreover, we also use the predictive power of the RF model to reconstruct the GCP-PC global map given the retained top geography and climate predictors, utilising the k-fold approach. Variable ranking and GCP per capita prediction Global GCP per capita We start by presenting the comparison of the performance of the three statistical models tested: RF, GB and ML. Specifically, we run a comparison between RF and GB keeping all the 121 variables, using the k-fold validation approach, as well as with the top 10 predictors. The ML model is tested with the 10 selected predictors to avoid collinearities issues. As shown in Table 3, the RF’s error is less than half that of GB in terms of the normalised Mean Absolute Error (nMAE, i.e. MAE divided by the standard deviation of the log10 GCP-PC distribution). Similarly to the case with all variables, the RF performance for the top 10 predictors is more than twice as better than that of GB. While the first comparison, with all the variables, is more

representative as the selection of 10 predictors has been made using the RF model, even the nMAE for the RF’s 10 predictors is distinctly lower than the GB’s 121 predictors. ML performs considerably worse than either RF and GB: the nMAE for ML is almost four times larger than that of RF. Tests with ML have been conducted also with 50 or 100 variables, in bootstrap PLOS ONE Effect of geography on fine resolution economy PLOS ONE | https://doi.org/10.1371/journal.pone.0229243 March 2, 2020 7 / 20