Calculation of variable importance for regression and classification models
A generic method for calculating variable importance for objects produced by
train and method specific methods
# S3 method for bagEarth varImp(object, ...)
# S3 method for bagFDA varImp(object, ...)
# S3 method for C5.0 varImp(object, ...)
# S3 method for cubist varImp(object, weights = c(0.5, 0.5), ...)
# S3 method for dsa varImp(object, cuts = NULL, ...)
# S3 method for glm varImp(object, ...)
# S3 method for glmnet varImp(object, lambda = NULL, ...)
# S3 method for JRip varImp(object, ...)
# S3 method for multinom varImp(object, ...)
# S3 method for nnet varImp(object, ...)
# S3 method for avNNet varImp(object, ...)
# S3 method for PART varImp(object, ...)
# S3 method for RRF varImp(object, ...)
# S3 method for rpart varImp(object, surrogates = FALSE, competes = TRUE, ...)
# S3 method for randomForest varImp(object, ...)
# S3 method for gbm varImp(object, numTrees = NULL, ...)
# S3 method for classbagg varImp(object, ...)
# S3 method for regbagg varImp(object, ...)
# S3 method for pamrtrained varImp(object, threshold, data, ...)
# S3 method for lm varImp(object, ...)
# S3 method for mvr varImp(object, estimate = NULL, ...)
# S3 method for earth varImp(object, value = "gcv", ...)
# S3 method for RandomForest varImp(object, ...)
# S3 method for plsda varImp(object, ...)
# S3 method for fda varImp(object, value = "gcv", ...)
# S3 method for gam varImp(object, ...)
# S3 method for Gam varImp(object, ...)
# S3 method for train varImp(object, useModel = TRUE, nonpara = TRUE, scale = TRUE, ...)
an object corresponding to a fitted model
parameters to pass to the specific
a numeric vector of length two that weighs the usage of variables in the rule conditions and the usage in the linear models (see details below).
the number of rule sets to use in the model (for
a single value of the penalty parameter
should surrogate splits contribute to the importance calculation?
should competing splits contribute to the importance calculation?
the number of iterations (trees) to use in a boosted tree model
the shrinkage threshold (
the training set predictors (
which estimate of performance should be used? See
the statistic that will be used to calculate importance: either
use a model based technique for measuring variable importance? This is only used for some models (lm, pls, rf, rpart, gbm, pam and mars)
should nonparametric methods be used to assess the relationship between the features and response (only used with
useModel = FALSEand only passed to
should the importance values be scaled to 0 and 100?
For models that do not have corresponding
varImp methods, see
Linear Models: the absolute value of the t--statistic for each model parameter is used.
glmnet: the absolute value of the coefficients
corresponding the the tuned model are used.
varImp.RandomForest are wrappers around the importance functions from
the randomForest and party packages, respectively.
Partial Least Squares: the variable importance measure here is based on weighted sums of the absolute regression coefficients. The weights are a function of the reduction of the sums of squares across the number of PLS components and are computed separately for each outcome. Therefore, the contribution of the coefficients are weighted proportionally to the reduction in the sums of squares.
Recursive Partitioning: The reduction in the loss function (e.g. mean
squared error) attributed to each variable at each split is tabulated and
the sum is returned. Also, since there may be candidate variables that are
important but are not used in a split, the top competing variables are also
tabulated at each split. This can be turned off using the
rpart.control. This method does not currently provide
class--specific measures of importance when the response is a factor.
Bagged Trees: The same methodology as a single tree is applied to all bootstrapped trees and the total importance is returned
varImp.gbm is a wrapper around the function
from that package (see the gbm package vignette)
Multivariate Adaptive Regression Splines: MARS models include a
backwards elimination feature selection routine that looks at reductions in
the generalized cross-validation (GCV) estimate of error. The
function tracks the changes in model statistics, such as the GCV, for each
predictor and accumulates the reduction in the statistic when each
predictor's feature is added to the model. This total reduction is used as
the variable importance measure. If a predictor was never used in any of the
MARS basis functions in the final model (after pruning), it has an
importance value of zero. Prior to June 2008, the package used an internal
function for these calculations. Currently, the
varImp is a wrapper
evimp function in the
There are three statistics that can be used to estimate variable importance
in MARS models. Using
varImp(object, value = "gcv") tracks the
reduction in the generalized cross-validation statistic as terms are added.
However, there are some cases when terms are retained in the model that
result in an increase in GCV. Negative variable importance values for MARS
are set to zero. Alternatively, using
varImp(object, value = "rss")
monitors the change in the residual sums of squares (RSS) as terms are
added, which will never be negative. Also, the option
value =" nsubsets"), which counts the number of subsets where the variable
is used (in the final, pruned model).
Nearest shrunken centroids: The difference between the class
centroids and the overall centroid is used to measure the variable influence
pamr.predict). The larger the difference between the class
centroid and the overall center of the data, the larger the separation
between the classes. The training set predictions must be supplied when an
object of class
pamrtrained is given to
Cubist: The Cubist output contains variable usage statistics. It
gives the percentage of times where each variable was used in a condition
and/or a linear model. Note that this output will probably be inconsistent
with the rules shown in the output from
summary.cubist. At each split of the tree, Cubist
saves a linear model (after feature selection) that is allowed to have terms
for each variable used in the current split or any split above it. Quinlan
(1992) discusses a smoothing algorithm where each model prediction is a
linear combination of the parent and child model along the tree. As such,
the final prediction is a function of all the linear models from the initial
node to the terminal node. The percentages shown in the Cubist output
reflects all the models involved in prediction (as opposed to the terminal
models shown in the output). The variable importance used here is a linear
combination of the usage in the rule conditions and the model.
PART and JRip: For these rule-based models, the importance for a predictor is simply the number of rules that involve the predictor.
C5.0: C5.0 measures predictor importance by determining the
percentage of training set samples that fall into all the terminal nodes
after the split. For example, the predictor in the first split automatically
has an importance measurement of 100 percent since all samples are affected
by this split. Other predictors may be used frequently in splits, but if the
terminal nodes cover only a handful of training set samples, the importance
scores may be close to zero. The same strategy is applied to rule-based
models and boosted versions of the model. The underlying function can also
return the number of times each predictor was involved in a split by using
metric = "usage".
Neural Networks: The method used here is based on Gevrey et al (2003), which uses combinations of the absolute values of the weights. For classification models, the class-specific importances will be the same.
Recursive Feature Elimination: Variable importance is computed using the ranking method used for feature selection. For the final subset size, the importances for the models across all resamples are averaged to compute an overall value.
Feature Selection via Univariate Filters, the percentage of resamples that a predictor was selected is determined. In other words, an importance of 0.50 means that the predictor survived the filter in half of the resamples.
A data frame with class
c("varImp.train", "data.frame") for
varImp.train or a matrix for other models.
Gevrey, M., Dimopoulos, I., & Lek, S. (2003). Review and comparison of methods to study the contribution of variables in artificial neural network models. Ecological Modelling, 160(3), 249-264.
Quinlan, J. (1992). Learning with continuous classes. Proceedings of the 5th Australian Joint Conference On Artificial Intelligence, 343-348.