Abstract
In an interesting and quite exhaustive review on Random Forests (RF) methodology in bioinformatics Touw et al. address—among other topics—the problem of the detection of interactions between variables based on RF methodology. We feel that some important statistical concepts, such as ‘interaction’, ‘conditional dependence’ or ‘correlation’, are sometimes employed inconsistently in the bioinformatics literature in general and in the literature on RF in particular. In this letter to the Editor, we aim to clarify some of the central statistical concepts and point out some confusing interpretations concerning RF given by Touw et al. and other authors.
Highlights
Random Forests (RF) is a valuable analysis tool, especially in situations where datasets contain many variables with complex relationships
We will give a consistent statistical definition of those concepts that are most central for understanding the rationale and behavior of RF
Our intention is not to impose our definitions on everyone but rather to provide a possible interpretation of the considered concepts that allows a better understanding of some aspects of RF methodology
Summary
Random Forests (RF) is a valuable analysis tool, especially in situations where datasets contain many variables with complex relationships. This behavior is not outright wrong, because there are different concepts for judging the importance of a variable in the presence of associations/correlations among the predictor variables (see, for example [20]) It is not the behavior a user may expect when he/she is used to the partial or conditional behavior of the regression coefficients in (generalized) linear models that was outlined in the section ‘Interactions in regression models’. The marginal or unconditional view is inherent in the standard RF importance measure and in correlations between one predictor variable and the response variable without taking potential confounders into account This principle can again be illustrated by recalling the model formula for the logistic regression model with the two predictor variables X2 (trained staff) and X3 (clean hospital floors) which do not interact: logit1⁄2PðY 1⁄4 1jX2 1⁄4 x2,X3 1⁄4 x3Þ. Does it relate to the ability of RF to yield high individual VIMs for predictor variables involved in interactions [31], the possibility to directly identify which predictor variables interact with each other by examining a RF [32, 1], or the combination of RF with other analysis tools with the aim of identifying interactions [30]? In any case, when an algorithm based on RF (possibly combined with other tools) is suggested to identify which predictor variables interact with each other, we claim that this algorithm should be assessed in simulations using adequate measures such as, for example, sensitivity, the proportion of pairs of interacting variables that are correctly identified as interacting; specificity, the proportion of pairs of non-interacting variables that are correctly identified as non-interacting; or false positive rate, the proportion of pairs of noninteracting variables within the pairs identified as interacting
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