Package 'leaps'

all-subsets regressiom

Description

leaps() performs an exhaustive search for the best subsets of the variables in x for predicting y in linear regression, using an efficient branch-and-bound algorithm. It is a compatibility wrapper for regsubsets does the same thing better.

Since the algorithm returns a best model of each size, the results do not depend on a penalty model for model size: it doesn't make any difference whether you want to use AIC, BIC, CIC, DIC, ...

Usage

leaps(x=, y=, wt=rep(1, NROW(x)), int=TRUE, method=c("Cp", "adjr2", "r2"), nbest=10,
 names=NULL, df=NROW(x), strictly.compatible=TRUE)

Arguments

x	A matrix of predictors
y	A response vector
wt	Optional weight vector
int	Add an intercept to the model
method	Calculate Cp, adjusted R-squared or R-squared
nbest	Number of subsets of each size to report
names	vector of names for columns of x
df	Total degrees of freedom to use instead of nrow(x) in calculating Cp and adjusted R-squared
strictly.compatible	Implement misfeatures of leaps() in S

Value

A list with components

which	logical matrix. Each row can be used to select the columns of x in the respective model
size	Number of variables, including intercept if any, in the model
cp	or adjr2 or r2 is the value of the chosen model selection statistic for each model
label	vector of names for the columns of x

Note

With strictly.compatible=T the function will stop with an error if x is not of full rank or if it has more than 31 columns. It will ignore the column names of x even if names==NULL and will replace them with "0" to "9", "A" to "Z".

References

Alan Miller "Subset Selection in Regression" Chapman & Hall

See Also

regsubsets, regsubsets.formula, regsubsets.default

Examples

x<-matrix(rnorm(100),ncol=4)
y<-rnorm(25)
leaps(x,y)

---

Internal functions for leaps(), subsets()

Description

These functions are used internally by regsubsets and leaps. They are wrappers for Fortran routines that construct and manipulate a QR decomposition.

Usage

leaps.setup(x,y,wt=rep(1,length(y)),force.in=NULL,force.out=NULL,intercept=TRUE,nvmax=8,
  nbest=1,warn.dep=TRUE)
leaps.seqrep(leaps.obj)
leaps.exhaustive(leaps.obj,really.big=FALSE)
leaps.backward(leaps.obj,nested)
leaps.forward(leaps.obj,nested)

Arguments

x	A matrix of predictors
y	A response vector
wt	Optional weight vector
intercept	Add an intercept to the model
force.in	vector indicating variable that must be in the model
force.out	vector indicating variable that must not be in the model
nbest	Number of subsets of each size to report
nvmax	largest subset size to examine
warn.dep	warn if x is not of full rank
leaps.obj	An object of class leaps as produced by leaps.setup
really.big	required before R gets sent off on a long uninterruptible computation
nested	Use just the forward or backward selection models, not the models with variables 1:nvmax constructed for free in the setup

See Also

regsubsets, leaps

---

Graphical table of best subsets

Description

Plots a table of models showing which variables are in each model. The models are ordered by the specified model selection statistic. This plot is particularly useful when there are more than ten or so models and the simple table produced by summary.regsubsets is too big to read.

Usage

## S3 method for class 'regsubsets'
plot(x, labels=obj$xnames, main=NULL, scale=c("bic", "Cp", "adjr2", "r2"),
col=gray(seq(0, 0.9, length = 10)),...)

Arguments

x	regsubsets object
labels	variable names
main	title for plot
scale	which summary statistic to use for ordering plots
col	Colors: the last color should be close to but distinct from white
...	other arguments

Value

None

Author(s)

Thomas Lumley, based on a concept by Merlise Clyde

See Also

regsubsets,summary.regsubsets

Examples

data(swiss)
a<-regsubsets(Fertility~.,nbest=3,data=swiss)
par(mfrow=c(1,2))
plot(a)
plot(a,scale="r2")

---

functions for model selection

Description

Model selection by exhaustive search, forward or backward stepwise, or sequential replacement

Usage

regsubsets(x=, ...)

## S3 method for class 'formula'
regsubsets(x=, data=, weights=NULL, nbest=1, nvmax=8,
 force.in=NULL, force.out=NULL, intercept=TRUE,
 method=c("exhaustive", "backward", "forward", "seqrep"),
 really.big=FALSE,
 nested=(nbest==1),...)

## Default S3 method:
regsubsets(x=, y=, weights=rep(1, length(y)), nbest=1, nvmax=8,
force.in=NULL, force.out=NULL, intercept=TRUE,
 method=c("exhaustive","backward", "forward", "seqrep"),
really.big=FALSE,nested=(nbest==1),...)

## S3 method for class 'biglm'
regsubsets(x,nbest=1,nvmax=8,force.in=NULL,
method=c("exhaustive","backward", "forward", "seqrep"),
really.big=FALSE,nested=(nbest==1),...)

## S3 method for class 'regsubsets'
summary(object,all.best=TRUE,matrix=TRUE,matrix.logical=FALSE,df=NULL,...)

## S3 method for class 'regsubsets'
coef(object,id,vcov=FALSE,...)
## S3 method for class 'regsubsets'
vcov(object,id,...)

Arguments

x	design matrix or model formula for full model, or biglm object
data	Optional data frame
y	response vector
weights	weight vector
nbest	number of subsets of each size to record
nvmax	maximum size of subsets to examine
force.in	index to columns of design matrix that should be in all models
force.out	index to columns of design matrix that should be in no models
intercept	Add an intercept?
method	Use exhaustive search, forward selection, backward selection or sequential replacement to search.
really.big	Must be TRUE to perform exhaustive search on more than 50 variables.
nested	See the Note below: if nested=FALSE, models with columns 1, 1 and 2, 1-3, and so on, will also be considered
object	regsubsets object
all.best	Show all the best subsets or just one of each size
matrix	Show a matrix of the variables in each model or just summary statistics
matrix.logical	With matrix=TRUE, the matrix is logical TRUE/FALSE or string "*"/" "
df	Specify a number of degrees of freedom for the summary statistics. The default is n-1
id	Which model or models (ordered as in the summary output) to return coefficients and variance matrix for
vcov	If TRUE, return the variance-covariance matrix as an attribute
...	Other arguments for future methods

Details

Since this function returns separate best models of all sizes up to nvmax and since different model selection criteria such as AIC, BIC, CIC, DIC, ... differ only in how models of different sizes are compared, the results do not depend on the choice of cost-complexity tradeoff.

When x is a biglm object it is assumed to be the full model, so force.out is not relevant. If there is an intercept it is forced in by default; specify a force.in as a logical vector with FALSE as the first element to allow the intercept to be dropped.

The model search does not actually fit each model, so the returned object does not contain coefficients or standard errors. Coefficients and the variance-covariance matrix for one or model models can be obtained with the coef and vcov methods.

Value

regsubsets returns an object of class "regsubsets" containing no user-serviceable parts. It is designed to be processed by summary.regsubsets.

summary.regsubsets returns an object with elements

which	A logical matrix indicating which elements are in each model
rsq	The r-squared for each model
rss	Residual sum of squares for each model
adjr2	Adjusted r-squared
cp	Mallows' Cp
bic	Schwartz's information criterion, BIC
outmat	A version of the which component that is formatted for printing
obj	A copy of the regsubsets object

The coef method returns a coefficient vector or list of vectors, the vcov method returns a matrix or list of matrices.

Note

As part of the setup process, the code initially fits models with the first variable in x, the first two, the first three, and so on. For forward and backward selection it is possible that the model with the k first variables will be better than the model with k variables from the selection algorithm. If it is, the model with the first k variables will be returned, with a warning. This can happen for forward and backward selection. It (obviously) can't for exhaustive search.

With nbest=1 you can avoid these extra models with nested=TRUE, which is the default.

See Also

leaps

Examples

data(swiss)
a<-regsubsets(as.matrix(swiss[,-1]),swiss[,1])
summary(a)
b<-regsubsets(Fertility~.,data=swiss,nbest=2)
summary(b)

coef(a, 1:3)
vcov(a, 3)

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