uc.lars: Maximum Likelihood Least Angle Regression on Uncorrelated...

In RXshrink: Maximum Likelihood Shrinkage using Generalized Ridge or Least Angle Regression

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)

RXshrink documentation built on Aug. 8, 2023, 1:09 a.m.