Classification and Regression with Random Forest
Description
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.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17  ## S3 method for class 'formula'
randomForest(formula, data=NULL, ..., subset, na.action=na.fail)
## Default S3 method:
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,
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, maxLevel=0, keep.group=FALSE,
corr.threshold=1, corr.method="pearson", ...)
## S3 method for class 'randomForest'
print(x, ...)

Arguments
data 
an optional data frame containing the variables in the model.
By default the variables are taken from the environment which

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

y 
A response vector. If a factor, classification is assumed,
otherwise regression is assumed. If omitted, 
xtest 
a data frame or matrix (like 
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 
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). 
importance 
Should importance of predictors be assessed? 
localImp 
Should casewise importance measure be computed?
(Setting this to 
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 
do.trace 
If set to 
keep.forest 
If set to 
corr.bias 
perform bias correction for regression? Note: Experimental. Use at your own risk. 
keep.inbag 
Should an 
maxLevel 
If 
corr.threshold 
If 
corr.method 
Method for computing correlation between variables.
Default 
keep.group 
If 
... 
optional parameters to be passed to the low level function

Value
An object of class randomForest
, which is a list with the
following components:
call 
the original call to 
type 
one of 
predicted 
the predicted values of the input data based on outofbag samples. 
importance 
a matrix with 
importanceSD 
The “standard errors” of the permutationbased
importance measure. For classification, a 
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. 
ntree 
number of trees grown. 
mtry 
number of predictors sampled for spliting at each node. 
forest 
(a list that contains the entire forest; 
err.rate 
(classification only) vector error rates of the prediction on the input data, the ith element being the error rate for all trees up to the ith. 
confusion 
(classification only) the confusion matrix of the prediction. 
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 ‘votes’ from the random forest. 
oob.times 
number of times cases are ‘outofbag’ (and thus used in computing OOB error estimate) 
proximity 
if 
mse 
(regression only) vector of mean square errors: sum of squared
residuals divided by 
rsq 
(regression only) “pseudo Rsquared”: 1  
test 
if test set is given (through the 
group 
matrix the same shape as 
permX 
permuted 
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.
Author(s)
Andy Liaw andy\_liaw@merck.com and Matthew Wiener matthew\_wiener@merck.com, based on original Fortran code by Leo Breiman and Adele Cutler.
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”, http://oz.berkeley.edu/users/breiman/Using_random_forests_V3.1.pdf.
See Also
predict.randomForest
, varImpPlot
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46  ## 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)
## 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(32, 5), x2=runif(160), y=rnorm(160))
(rf1 < randomForest(x[3], x[[3]], ntree=10))
