randomForest
Classification and Regression with Random Forest
randomForest
implements Breiman's random forest algorithm (based on
Breiman and Cutler's original Fortran code) for classification and
regression. It can also be used in unsupervised mode for assessing
proximities among data points.
 Keywords
 regression, classif, tree
Usage
"randomForest"(formula, data=NULL, ..., subset, na.action=na.fail)
"randomForest"(x, y=NULL, xtest=NULL, ytest=NULL, ntree=500, mtry=if (!is.null(y) && !is.factor(y)) max(floor(ncol(x)/3), 1) else floor(sqrt(ncol(x))), replace=TRUE, classwt=NULL, cutoff, strata, sampsize = if (replace) nrow(x) else ceiling(.632*nrow(x)), nodesize = if (!is.null(y) && !is.factor(y)) 5 else 1, maxnodes = NULL, importance=FALSE, localImp=FALSE, nPerm=1, proximity, oob.prox=proximity, norm.votes=TRUE, do.trace=FALSE, keep.forest=!is.null(y) && is.null(xtest), corr.bias=FALSE, keep.inbag=FALSE, ...)
"print"(x, ...)
Arguments
 data
 an optional data frame containing the variables in the model.
By default the variables are taken from the environment which
randomForest
is called from.  subset
 an index vector indicating which rows should be used. (NOTE: If given, this argument must be named.)
 na.action
 A function to specify the action to be taken if NAs are found. (NOTE: If given, this argument must be named.)
 x, formula
 a data frame or a matrix of predictors, or a formula
describing the model to be fitted (for the
print
method, anrandomForest
object).  y
 A response vector. If a factor, classification is assumed,
otherwise regression is assumed. If omitted,
randomForest
will run in unsupervised mode.  xtest
 a data frame or matrix (like
x
) containing predictors for the test set.  ytest
 response for the test set.
 ntree
 Number of trees to grow. This should not be set to too small a number, to ensure that every input row gets predicted at least a few times.
 mtry
 Number of variables randomly sampled as candidates at each
split. Note that the default values are different for
classification (sqrt(p) where p is number of variables in
x
) and regression (p/3)  replace
 Should sampling of cases be done with or without replacement?
 classwt
 Priors of the classes. Need not add up to one. Ignored for regression.
 cutoff
 (Classification only) A vector of length equal to number of classes. The `winning' class for an observation is the one with the maximum ratio of proportion of votes to cutoff. Default is 1/k where k is the number of classes (i.e., majority vote wins).
 strata
 A (factor) variable that is used for stratified sampling.
 sampsize
 Size(s) of sample to draw. For classification, if sampsize is a vector of the length the number of strata, then sampling is stratified by strata, and the elements of sampsize indicate the numbers to be drawn from the strata.
 nodesize
 Minimum size of terminal nodes. Setting this number larger causes smaller trees to be grown (and thus take less time). Note that the default values are different for classification (1) and regression (5).
 maxnodes
 Maximum number of terminal nodes trees in the forest
can have. If not given, trees are grown to the maximum possible
(subject to limits by
nodesize
). If set larger than maximum possible, a warning is issued.  importance
 Should importance of predictors be assessed?
 localImp
 Should casewise importance measure be computed?
(Setting this to
TRUE
will overrideimportance
.)  nPerm
 Number of times the OOB data are permuted per tree for assessing variable importance. Number larger than 1 gives slightly more stable estimate, but not very effective. Currently only implemented for regression.
 proximity
 Should proximity measure among the rows be calculated?
 oob.prox
 Should proximity be calculated only on ``outofbag'' data?
 norm.votes
 If
TRUE
(default), the final result of votes are expressed as fractions. IfFALSE
, raw vote counts are returned (useful for combining results from different runs). Ignored for regression.  do.trace
 If set to
TRUE
, give a more verbose output asrandomForest
is run. If set to some integer, then running output is printed for everydo.trace
trees.  keep.forest
 If set to
FALSE
, the forest will not be retained in the output object. Ifxtest
is given, defaults toFALSE
.  corr.bias
 perform bias correction for regression? Note: Experimental. Use at your own risk.
 keep.inbag
 Should an
n
byntree
matrix be returned that keeps track of which samples are ``inbag'' in which trees (but not how many times, if sampling with replacement)  ...
 optional parameters to be passed to the low level function
randomForest.default
.
Value

An object of class
 call
 the original call to
randomForest
 type
 one of
regression
,classification
, orunsupervised
.  predicted
 the predicted values of the input data based on outofbag samples.
 importance
 a matrix with
nclass
+ 2 (for classification) or two (for regression) columns. For classification, the firstnclass
columns are the classspecific measures computed as mean descrease in accuracy. Thenclass
+ 1st column is the mean descrease in accuracy over all classes. The last column is the mean decrease in Gini index. For Regression, the first column is the mean decrease in accuracy and the second the mean decrease in MSE. Ifimportance=FALSE
, the last measure is still returned as a vector.  importanceSD
 The ``standard errors'' of the permutationbased
importance measure. For classification, a
p
bynclass + 1
matrix corresponding to the firstnclass + 1
columns of the importance matrix. For regression, a lengthp
vector.  localImp
 a p by n matrix containing the casewise importance
measures, the [i,j] element of which is the importance of ith
variable on the jth case.
NULL
iflocalImp=FALSE
.  ntree
 number of trees grown.
 mtry
 number of predictors sampled for spliting at each node.
 forest
 (a list that contains the entire forest;
NULL
ifrandomForest
is run in unsupervised mode or ifkeep.forest=FALSE
.  err.rate
 (classification only) vector error rates of the prediction on the input data, the ith element being the (OOB) error rate for all trees up to the ith.
 confusion
 (classification only) the confusion matrix of the prediction (based on OOB data).
 votes
 (classification only) a matrix with one row for each input data point and one column for each class, giving the fraction or number of (OOB) `votes' from the random forest.
 oob.times
 number of times cases are `outofbag' (and thus used in computing OOB error estimate)
 proximity
 if
proximity=TRUE
whenrandomForest
is called, a matrix of proximity measures among the input (based on the frequency that pairs of data points are in the same terminal nodes).  mse
 (regression only) vector of mean square errors: sum of squared
residuals divided by
n
.  rsq
 (regression only) ``pseudo Rsquared'': 1 
mse
/ Var(y).  test
 if test set is given (through the
xtest
or additionallyytest
arguments), this component is a list which contains the correspondingpredicted
,err.rate
,confusion
,votes
(for classification) orpredicted
,mse
andrsq
(for regression) for the test set. Ifproximity=TRUE
, there is also a component,proximity
, which contains the proximity among the test set as well as proximity between test and training data.
randomForest
, which is a list with the
following components:Note
The forest
structure is slightly different between
classification and regression. For details on how the trees are
stored, see the help page for getTree
.
If xtest
is given, prediction of the test set is done ``in
place'' as the trees are grown. If ytest
is also given, and
do.trace
is set to some positive integer, then for every
do.trace
trees, the test set error is printed. Results for the
test set is returned in the test
component of the resulting
randomForest
object. For classification, the votes
component (for training or test set data) contain the votes the cases
received for the classes. If norm.votes=TRUE
, the fraction is
given, which can be taken as predicted probabilities for the classes.
For large data sets, especially those with large number of variables,
calling randomForest
via the formula interface is not advised:
There may be too much overhead in handling the formula.
The ``local'' (or casewise) variable importance is computed as follows: For classification, it is the increase in percent of times a case is OOB and misclassified when the variable is permuted. For regression, it is the average increase in squared OOB residuals when the variable is permuted.
References
Breiman, L. (2001), Random Forests, Machine Learning 45(1), 532.
Breiman, L (2002), ``Manual On Setting Up, Using, And Understanding Random Forests V3.1'', https://www.stat.berkeley.edu/~breiman/Using_random_forests_V3.1.pdf.
See Also
Examples
library(randomForest)
## Classification:
##data(iris)
set.seed(71)
iris.rf < randomForest(Species ~ ., data=iris, importance=TRUE,
proximity=TRUE)
print(iris.rf)
## Look at variable importance:
round(importance(iris.rf), 2)
## Do MDS on 1  proximity:
iris.mds < cmdscale(1  iris.rf$proximity, eig=TRUE)
op < par(pty="s")
pairs(cbind(iris[,1:4], iris.mds$points), cex=0.6, gap=0,
col=c("red", "green", "blue")[as.numeric(iris$Species)],
main="Iris Data: Predictors and MDS of Proximity Based on RandomForest")
par(op)
print(iris.mds$GOF)
## The `unsupervised' case:
set.seed(17)
iris.urf < randomForest(iris[, 5])
MDSplot(iris.urf, iris$Species)
## stratified sampling: draw 20, 30, and 20 of the species to grow each tree.
(iris.rf2 < randomForest(iris[1:4], iris$Species,
sampsize=c(20, 30, 20)))
## Regression:
## data(airquality)
set.seed(131)
ozone.rf < randomForest(Ozone ~ ., data=airquality, mtry=3,
importance=TRUE, na.action=na.omit)
print(ozone.rf)
## Show "importance" of variables: higher value mean more important:
round(importance(ozone.rf), 2)
## "x" can be a matrix instead of a data frame:
set.seed(17)
x < matrix(runif(5e2), 100)
y < gl(2, 50)
(myrf < randomForest(x, y))
(predict(myrf, x))
## "complicated" formula:
(swiss.rf < randomForest(sqrt(Fertility) ~ .  Catholic + I(Catholic < 50),
data=swiss))
(predict(swiss.rf, swiss))
## Test use of 32level factor as a predictor:
set.seed(1)
x < data.frame(x1=gl(53, 10), x2=runif(530), y=rnorm(530))
(rf1 < randomForest(x[3], x[[3]], ntree=10))
## Grow no more than 4 nodes per tree:
(treesize(randomForest(Species ~ ., data=iris, maxnodes=4, ntree=30)))
## test proximity in regression
iris.rrf < randomForest(iris[1], iris[[1]], ntree=101, proximity=TRUE, oob.prox=FALSE)
str(iris.rrf$proximity)