Random forest for ordinal responses: Prediction and variable selection

The random forest method is a commonly used tool for classification with high-dimensional data that is able to rank candidate predictors through its inbuilt variable importance measures. It can be applied to various kinds of regression problems including nominal, metric and survival response variables. While classification and regression problems using random forest methodology have been extensively investigated in the past, in the case of ordinal response there is no standard procedure. Extensive studies using random forest based on conditional inference trees are conducted to explore whether incorporating the ordering information yields any improvement in both prediction performance or variable selection. Two novel permutation variable importance measures are presented that are reasonable alternatives to the currently implemented importance measure which was developed for nominal response and makes no use of the ordering in the levels of an ordinal response variable. Results based on simulated and real data suggest that predictor rankings can be improved in some settings by using new permutation importance measures that explicitly use the ordering in the response levels in combination with ordinal regression trees. With respect to prediction accuracy, the performance of ordinal regression trees was similar to and in most settings even slightly better than that of classification trees.