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

Value

A list with components

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

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

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

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

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)