Finally, the (total)
PCP was calculated as the number of correctly predicted cases
divided by the total number of cases. In addition, the percentage of
correctly predicted area under the curve (AUC) of the relative
operating characteristic (ROC) was calculated (Crk et al., 2009). The
ROC curve was plotted with the sensitivity (true positive rate)
versus 1-the specificity (false positive rate) for every possible cutoff
that could be chosen to convert the predicted probability of urban
expansion into the actual degree of urbanization. The AUCwas then
calculated as a measure of the probability of the model to render
a higher predicted value of urbanization for a pixel that underwent
urbanization than for those that did not. An AUC value approaching
1 indicates perfect performance of the model.