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The package ranger implements random forests in R. Among other things, the function used to fit a random forest allows to choose among several splitting rules, and several ways to compute the importance of the features. The documentation says:

For importance:

Variable importance mode, one of 'none', 'impurity', 'impurity_corrected', 'permutation'. The 'impurity' measure is the Gini index for classification, the variance of the responses for regression and the sum of test statistics (see splitrule) for survival.

What is impurity_corrected? I understand that impurity in regression is a measure based on the variance reduction for each split where the considered variable is used, but how is it corrected?

For splitting rules:

Splitting rule. For classification and probability estimation "gini", "extratrees" or "hellinger" with default "gini". For regression "variance", "extratrees", "maxstat" or "beta" with default "variance". For survival "logrank", "extratrees", "C" or "maxstat" with default "logrank".

What are maxstat and beta splitting rules in a regression setting?

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    $\begingroup$ impurity_corrected is discussed in the documentation, with a reference to Nembrini et al. (2018). $\endgroup$ Commented Dec 7, 2022 at 15:16
  • $\begingroup$ Don't trust any ranger result until you produce an unbiased high-resolution calibration curve. I have seen an astounding amount of overfitting in using ranger, and this is reflected by overproduction (low predicted values are too low, high ones are too high). $\endgroup$ Commented Apr 27 at 12:06

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I think it refers to maximally selected rank statistics. There is a paper talking about it : https://arxiv.org/pdf/1605.03391.pdf.

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