uc.lars {RXshrink}

Maximum Likelihood Least Angle Regression on Uncorrelated X-Components

Description

Apply least angle regression estimation to the uncorrelated components of a possibly ill-conditioned linear regression model and generate normal-theory maximum likelihood TRACE displays.

Usage

  uc.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 uc.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

uc.lars() applies Least Angle Regression to the uncorrelated components of a possibly ill-conditioned set of x-variables. A closed-form expression for the lars/lasso shrinkage delta factors exits in this case: Delta(i) = max(0,1-k/abs[PC(i)]), where PC(i) is the principal correlation between y and the i-th principal coordinates of X. Note that the k-factor in this formulation is limited to a subset of [0,1]. MCAL=0 occurs at k=0, while MCAL = p results when k is the maximum absolute principal correlation.

Value

An output list object of class uc.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).

Author(s)

Bob Obenchain <[e-mail]>

References

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. (1994-2005) Shrinkage Regression: ridge, BLUP, Bayes, spline and Stein. http://localcontrolstatistics.org

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

See Also

aug.lars.

Examples

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