different information on the underlying data generation process. The random forests method essentially averages over many noisy but approximately unbiased and un-correlated trees to reduce the variance of the predictor (Breiman 2001a; Hastie et al. 2017). Following the literature, we considered a large number ( ) of binary classification trees for our urban classification problem, each of them ( ) grown on an independently bootstrapped subsample from the BB 1,277 sample of places. The bootstrapped subsample thus served as training data. For each tree we randomly selected out of the covariates in the full set, with the rule of thumb being that pp should be smaller than ~~√~~ to reduce the correlation between trees. We also set a predetermined number of nodes kk KK kk ( ) for each tree. Parameters , and characterize the forest. KK At each node of each tree, we chose the cutoff point of the selected covariate that ensured the greatest ll BB kk ll At each node of each tree, we chose the cutoff point of the selected covariate that ensured the greatest similarity among places in each of the two resulting groups, and the greatest diversity between places in the two groups. Similarity and diversity were evaluated based on the pooled classification of places, using the Gini index to identify the optimal cutoff point. We then considered the next node, again involving one of randomly selected covariates, and repeated the same steps. We continued the process recursively until the predetermined number of nodes was reached. kk Proceeding this way, each of the trees led to an unequivocal assessment of all places in the training ll subsample as either urban or rural. But such assessment is not necessarily the same as that resulting from BB the pooled classification. We then used the trees developed on each of the independently bootstrapped subsamples to the entire universe. By proceeding this way, all places in the universe were assessed BB times. The random forest predictor of the urban status of a place is derived by applying majority rule to these assessments. BB We tuned our random forests method by varying the number of trees (B) and the number of covariates BB to be randomly selected to develop each node ( ). We relied on the standard out-of-bag (OOB) error rate to evaluate the performance of different combinations of parameter values. We found that the OOB error rate is minimized as the number of trees considered increases above 300 and the number of covariates kk to be selected declines to two (appendix 4). In light of this, we choose 500 trees and two covariates at each node to implement the random forests model.

To facilitate the comparison with the results from the Logit model, we also considered multiple combinations of covariates. We focused on mean decrease accuracy and mean decrease Gini to evaluate their importance. Overall, built-up share and population size emerged as the most important predictors of urban status (appendix 5). This finding is consistent with the results from the Logit model. However, the relative importance of different covariates is only indicative. This is because the random forests method is a prediction tool, not an explanation tool, and the estimated relative importance of predictors is also sensitive to sample and process.

Again, we evaluated the prediction accuracy of the random forests method using the 10-fold crossvalidation procedure and found that it outperforms the Logit model (figure 5c). The percentage of observations correctly predicted reached 88.2 percent, 1 percentage point higher than with the bestperforming specification of the Logit model. And the confidence interval was comparable. However, the results from the random forests method are consistent with those from the Logit model in terms of the selection of covariates. Including all four key indicators significantly improves prediction accuracy over using indicators based exclusively on traditional or modern data. On the other hand, the addition of NDVI and NDWI indicators, and of higher-order terms, yields marginal gains.

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