# 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

```
# S3 method for formula
randomForest(formula, data=NULL, ..., subset, na.action=na.fail)
# S3 method for default
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, ...)
# S3 method for 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

`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, an`randomForest`

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 override`importance`

.)- 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 ``out-of-bag'' data?

- norm.votes
If

`TRUE`

(default), the final result of votes are expressed as fractions. If`FALSE`

, 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 as`randomForest`

is run. If set to some integer, then running output is printed for every`do.trace`

trees.- keep.forest
If set to

`FALSE`

, the forest will not be retained in the output object. If`xtest`

is given, defaults to`FALSE`

.- corr.bias
perform bias correction for regression? Note: Experimental. Use at your own risk.

- keep.inbag
Should an

`n`

by`ntree`

matrix be returned that keeps track of which samples are ``in-bag'' 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 `randomForest`

, which is a list with the
following components:

the original call to `randomForest`

one of `regression`

, `classification`

, or
`unsupervised`

.

the predicted values of the input data based on out-of-bag samples.

a matrix with `nclass`

+ 2 (for classification)
or two (for regression) columns. For classification, the first
`nclass`

columns are the class-specific measures computed as
mean descrease in accuracy. The `nclass`

+ 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.
If `importance=FALSE`

, the last measure is still returned as a
vector.

The ``standard errors'' of the permutation-based
importance measure. For classification, a `p`

by ```
nclass
+ 1
```

matrix corresponding to the first `nclass + 1`

columns
of the importance matrix. For regression, a length `p`

vector.

a p by n matrix containing the casewise importance
measures, the [i,j] element of which is the importance of i-th
variable on the j-th case. `NULL`

if `localImp=FALSE`

.

number of trees grown.

number of predictors sampled for spliting at each node.

(a list that contains the entire forest; `NULL`

if
`randomForest`

is run in unsupervised mode or if
`keep.forest=FALSE`

.

(classification only) vector error rates of the prediction on the input data, the i-th element being the (OOB) error rate for all trees up to the i-th.

(classification only) the confusion matrix of the prediction (based on OOB data).

(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.

number of times cases are `out-of-bag' (and thus used in computing OOB error estimate)

if `proximity=TRUE`

when
`randomForest`

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).

(regression only) vector of mean square errors: sum of squared
residuals divided by `n`

.

(regression only) ``pseudo R-squared'': 1 - `mse`

/
Var(y).

if test set is given (through the `xtest`

or additionally
`ytest`

arguments), this component is a list which contains the
corresponding `predicted`

, `err.rate`

, `confusion`

,
`votes`

(for classification) or `predicted`

, `mse`

and
`rsq`

(for regression) for the test set. If
`proximity=TRUE`

, there is also a component, `proximity`

,
which contains the proximity among the test set as well as proximity
between test and training data.

##### 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),
5-32.

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

```
# NOT RUN {
## 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 32-level 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)
# }
```

*Documentation reproduced from package randomForest, version 4.6-14, License: GPL (>= 2)*