LOST IN THE FOREST

Abstract

To date, there remains no satisfactory solution for absent levels in random forest models. Absent levels are levels of a predictor variable encountered during prediction for which no explicit rule exists. Imposing an order on nominal predictors allows absent levels to be integrated and used for prediction. The ordering of predictors has traditionally been via class probabilities with absent levels designated the lowest order. Using a combination of simulated data and pathogen source-attribution models using whole-genome sequencing data, we examine how the method of ordering predictors with absent levels can (i) systematically bias a model, and (ii) affect the out-of-bag error rate. We show that the traditional approach is systematically biased and underestimates out-of-bag error rates, and that this bias is resolved by ordering absent levels according to the a priori hypothesis of equal class probability. We present a novel method of ordering predictors via principal coordinates analysis (PCO) which capitalizes on the similarity between pairs of predictor levels. Absent levels are designated an order according to their similarity to each of the other levels in the training data. We show that the PCO method performs at least as well as the traditional approach of ordering and is not biased. the specification of predictor variables with absent levels as binary versus ordered affects the bias and accuracy of random forest models, and we present two alternate methods for ordering variable levels and dealing with absent levels. We examine the prediction accuracy and bias for source-attribution models of Campylobacter species using whole genome sequencing (WGS) data as a case study. We also present simulated data to detail how treatment of predictor variables as ordered versus unordered affects the OOB error rate.