lar: Least angle regression

In selectiveInference: Tools for Post-Selection Inference

Description

This function implements least angle regression, for use in the selectiveInference package

Usage

lar(x, y, maxsteps=2000, minlam=0, intercept=TRUE, normalize=TRUE,
    verbose=FALSE) 

Arguments

x	Matrix of predictors (n by p)
y	Vector of outcomes (length n)
maxsteps	Maximum number of steps to take
minlam	Minimum value of lambda to consider
intercept	Should an intercept be included on the model? Default is TRUE
normalize	Should the predictors be normalized? Default is TRUE
verbose	Print out progress along the way? Default is FALSE

Details

The least angle regression algorithm is described in detail by Efron et al. (2002). This function should match (in terms of its output) that from the lars package, but returns additional information (namely, the polyhedral constraints) needed for the selective inference calculations.

Value

lambda	Values of lambda (knots) visited along the path
action	Vector of predictors in order of entry
sign	Signs of coefficients of predictors, upon entry
df	Degrees of freedom of each active model
beta	Matrix of regression coefficients for each model along the path, one model per column
completepath	Was the complete stepwise path computed?
bls	If completepath is TRUE, the full least squares coefficients
Gamma	Matrix that captures the polyhedral selection at each step
nk	Number of polyhedral constraints at each step in path
vreg	Matrix of linear contrasts that gives coefficients of variables to enter along the path
mp	Value of M+ (for internal use with the spacing test)
x	Matrix of predictors used
y	Vector of outcomes used
bx	Vector of column means of original x
by	Mean of original y
sx	Norm of each column of original x
intercept	Was an intercept included?
normalize	Were the predictors normalized?
call	The call to lar

Author(s)

Ryan Tibshirani, Rob Tibshirani, Jonathan Taylor, Max G'Sell, Joshua Loftus, Stephen Reid

References

Brad Efron, Trevor Hastie, Iain Johnstone, and Rob Tibshirani (2002). Least angle regression. Annals of Statistics (with discussion).

See also the descriptions in Trevor Hastie, Rob Tibshirani, and Jerome Friedman (2002, 2009). Elements of Statistical Learning.

See Also

larInf, predict.lar, coef.lar, plot.lar

Examples

set.seed(43)
n = 50
p = 10
sigma = 1
x = matrix(rnorm(n*p),n,p)
beta = c(3,2,rep(0,p-2))
y = x%*%beta + sigma*rnorm(n)

# run LAR, plot results
larfit = lar(x,y)
plot(larfit)

# compute sequential p-values and confidence intervals
# (sigma estimated from full model)
out = larInf(larfit)
out                                    

selectiveInference documentation built on Sept. 7, 2019, 9:02 a.m.