Variable ranking and selection with random forest for unbalanced data

Abstract When one or several classes are much less prevalent than another class (unbalanced data), class error rates and variable importances of the machine learning algorithm random forest can be biased, particularly when sample sizes are smaller, imbalance levels higher, and effect sizes of important variables smaller. Using simulated data varying in size, imbalance level, number of true variables, their effect sizes, and the strength of multicollinearity between covariates, we evaluated how eight versions of random forest ranked and selected true variables out of a large number of covariates despite class imbalance. The version that calculated variable importance based on the area under the curve (AUC) was least adversely affected by class imbalance. For the same number of true variables, effect sizes, and multicollinearity between covariates, the AUC variable importance ranked true variables still highly at the lower sample sizes and higher imbalance levels at which the other seven versions no longer achieved high ranks for true variables. Conversely, using the Hellinger distance to split trees or downsampling the majority class already ranked true variables lower and more variably at the larger sample sizes and lower imbalance levels at which the other algorithms still ranked true variables highly. In variable selection, a higher proportion of true variables were identified when covariates were ranked by AUC importances and the proportion increased further when the AUC was used as the criterion in forward variable selection. In three case studies, known species–habitat relationships and their spatial scales were identified despite unbalanced data.