Variable Importance

Standard and conditional variable importance for `cforest', following the permutation principle of the `mean decrease in accuracy' importance in `randomForest'.

varimp(object, mincriterion = 0, conditional = FALSE, 
       threshold = 0.2, nperm = 1, OOB = TRUE, pre1.0_0 = conditional)

an object as returned by cforest.


the value of the test statistic or 1 - p-value that must be exceeded in order to include a split in the computation of the importance. The default mincriterion = 0 guarantees that all splits are included.


a logical determining whether unconditional or conditional computation of the importance is performed.


the threshold value for (1 - p-value) of the association between the variable of interest and a covariate, which must be exceeded inorder to include the covariate in the conditioning scheme for the variable of interest (only relevant if conditional = TRUE). A threshold value of zero includes all covariates.


the number of permutations performed.


a logical determining whether the importance is computed from the out-of-bag sample or the learning sample (not suggested).


Prior to party version 1.0-0, the actual data values were permuted according to the original permutation importance suggested by Breiman (2001). Now the assignments to child nodes of splits in the variable of interest are permuted as described by Hapfelmeier et al. (2012), which allows for missing values in the explanatory variables and is more efficient wrt memory consumption and computing time. This method does not apply to conditional variable importances.

Arguments to varImpAUC.


Function varimp can be used to compute variable importance measures similar to those computed by importance. Besides the standard version, a conditional version is available, that adjusts for correlations between predictor variables.

If conditional = TRUE, the importance of each variable is computed by permuting within a grid defined by the covariates that are associated (with 1 - p-value greater than threshold) to the variable of interest. The resulting variable importance score is conditional in the sense of beta coefficients in regression models, but represents the effect of a variable in both main effects and interactions. See Strobl et al. (2008) for details.

Note, however, that all random forest results are subject to random variation. Thus, before interpreting the importance ranking, check whether the same ranking is achieved with a different random seed -- or otherwise increase the number of trees ntree in ctree_control.

Note that in the presence of missings in the predictor variables the procedure described in Hapfelmeier et al. (2012) is performed.

Function varimpAUC is a wrapper for varImpAUC which implements AUC-based variables importances as described by Janitza et al. (2012). Here, the area under the curve instead of the accuracy is used to calculate the importance of each variable. This AUC-based variable importance measure is more robust towards class imbalance.

For right-censored responses, varimp uses the integrated Brier score as a risk measure for computing variable importances. This feature is extremely slow and experimental; use at your own risk.


A vector of `mean decrease in accuracy' importance scores.


Leo Breiman (2001). Random Forests. Machine Learning, 45(1), 5--32.

Alexander Hapfelmeier, Torsten Hothorn, Kurt Ulm, and Carolin Strobl (2012). A New Variable Importance Measure for Random Forests with Missing Data. Statistics and Computing,

Torsten Hothorn, Kurt Hornik, and Achim Zeileis (2006b). Unbiased Recursive Partitioning: A Conditional Inference Framework. Journal of Computational and Graphical Statistics, 15 (3), 651-674. Preprint available from

Silke Janitza, Carolin Strobl and Anne-Laure Boulesteix (2013). An AUC-based Permutation Variable Importance Measure for Random Forests. BMC Bioinformatics.2013, 14 119.

Carolin Strobl, Anne-Laure Boulesteix, Thomas Kneib, Thomas Augustin, and Achim Zeileis (2008). Conditional Variable Importance for Random Forests. BMC Bioinformatics, 9, 307.

  • varimp
  • varimpAUC
   set.seed(290875) <- cforest(score ~ ., data = readingSkills, 
       control = cforest_unbiased(mtry = 2, ntree = 50))

   # standard importance
   # the same modulo random variation
   varimp(, pre1.0_0 = TRUE)

   # conditional importance, may take a while...
   varimp(, conditional = TRUE)

# }
   data("GBSG2", package = "")
   ### add a random covariate for sanity check
   GBSG2$rand <- runif(nrow(GBSG2))
   object <- cforest(Surv(time, cens) ~ ., data = GBSG2, 
                     control = cforest_unbiased(ntree = 20)) 
   vi <- varimp(object)
   ### compare variable importances and absolute z-statistics
   barplot(abs(summary(coxph(Surv(time, cens) ~ ., data = GBSG2))$coeff[,"z"]))
   ### looks more or less the same
# }
Documentation reproduced from package party, version 1.3-1, License: GPL-2

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