aug.lars {RXshrink}

Maximum Likelihood Estimation of Effects in Least Angle Regression

Description

These functions perform calculations that determine whether least angle and lasso regression estimates correspond to generalized ridge regression (GRR) estimates (i.e. whether they use shrinkage delta-factors that are both non-negative and strictly less than 1.0). They also estimate the Normal-theory likelihood that MSE risk is minimized and compute diagnostics for display in ridge TRACE plots.

Usage

aug.lars(form, data, rscale = 1, type = "lar", trace = FALSE, 
    eps = .Machine$double.eps, omdmin = 9.9e-13) 

Arguments

form

A regression formula [y~x1+x2+...] suitable for use with lm().

data

Data frame containing observations on all variables in the formula.

rscale

One of three possible choices (0, 1 or 2) for "rescaling" of variables (after being "centered") to remove all "non-essential" ill-conditioning: 0 implies no rescaling; 1 implies divide each variable by its standard error; 2 implies rescale as in option 1 but re-express answers as in option 0.

type

One of "lasso", "lar" or "forward.stagewise" for function lars(). Names can be abbreviated to any unique substring. Default in aug.lars() is "lar".

trace

If TRUE, lars() function prints out its progress.

eps

The effective zero for lars().

omdmin

Strictly positive minimum allowed value for one-minus-delta (default = 9.9e-013.)

Details

aug.lars() calls the Efron/Hastie lars() function to perform Least Angle Regression on x-variables that have been centered and possibly rescaled but which may be (highly) correlated. Maximum likelihood TRACE displays paralleling those of eff.ridge() and qm.ridge() are also computed and (optionally) plotted.

Value

An output list object of class aug.lars:

form

The regression formula specified as the first argument.

data

Name of the data.frame object specified as the second argument.

p

Number of regression predictor variables.

n

Number of complete observations after removal of all missing values.

r2

Numerical value of R-square goodness-of-fit statistic.

s2

Numerical value of the residual mean square estimate of error.

prinstat

Listing of principal statistics.

gmat

Orthogonal matrix of direction cosines for regressor principal axes.

lars

An object of class lars.

coef

Matrix of shrinkage-ridge regression coefficient estimates.

risk

Matrix of MSE risk estimates for fitted coefficients.

exev

Matrix of excess MSE eigenvalues (ordinary least squares minus ridge.)

infd

Matrix of direction cosines for the estimated inferior direction, if any.

spat

Matrix of shrinkage pattern multiplicative delta factors.

mlik

Listing of criteria for maximum likelihood selection of M-extent-of-shrinkage.

sext

Listing of summary statistics for all M-extents-of-shrinkage.

mClk

Most Likely Extent of Shrinkage Observed: best multiple of (1/steps) <= p.

minC

Minimum Observed Value of Normal-theory -2*log(Likelihood-Ratio).

Author(s)

Bob Obenchain <[e-mail]>

References

Breiman L. (1995) Better subset regression using the non-negative garrote. Technometrics 37, 373-384.

Efron B, Hastie T, Johnstone I, Tibshirani R. (2003) Least angle regression. Annals of Statistics 32, 407-499.

Hastie T, Efron, B. (2013) lars: Least Angle Regression, Lasso and Forward Stagewise. ver 1.2, https://CRAN.R-project.org/package=lars

Obenchain RL. (2022) RXshrink_in_R.PDF RXshrink package vignette-like document, Version 2.1. http://localcontrolstatistics.org

Tibshirani R. (1996) Regression shrinkage and selection via the lasso. J. Roy. Stat. Soc. B 58, 267-288.

See Also

uc.lars.

Examples

  data(longley2)
  form <- GNP~GNP.deflator+Unemployed+Armed.Forces+Population+Year+Employed
  rxlobj <- aug.lars(form, data=longley2)
  rxlobj
  plot(rxlobj)
  str(rxlobj)