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.
uc.lars(form, data, rscale = 1, type = "lar", trace = FALSE,
eps = .Machine$double.eps, omdmin = 9.9e-13)An output list object of class uc.lars:
The regression formula specified as the first argument.
Name of the data.frame object specified as the second argument.
Number of regression predictor variables.
Number of complete observations after removal of all missing values.
Numerical value of R-square goodness-of-fit statistic.
Numerical value of the residual mean square estimate of error.
Listing of principal statistics.
Orthogonal matrix of direction cosines for regressor principal axes.
An object of class lars.
Matrix of shrinkage-ridge regression coefficient estimates.
Matrix of MSE risk estimates for fitted coefficients.
Matrix of excess MSE eigenvalues (ordinary least squares minus ridge.)
Matrix of direction cosines for the estimated inferior direction, if any.
Matrix of shrinkage pattern multiplicative delta factors.
Listing of criteria for maximum likelihood selection of M-extent-of-shrinkage.
Listing of summary statistics for all M-extents-of-shrinkage.
Most Likely Extent of Shrinkage Observed: best multiple of (1/steps) <= p.
Minimum Observed Value of Normal-theory -2*log(Likelihood).
A regression formula [y~x1+x2+...] suitable for use with lm().
Data frame containing observations on all variables in the formula.
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.
One of "lasso", "lar" or "forward.stagewise" for function lars(). Names can be abbreviated to any unique substring. Default in uc.lars() is "lar".
If TRUE, lars() function prints out its progress.
The effective zero for lars().
Strictly positive minimum allowed value for one-minus-delta (default = 9.9e-013.)
Bob Obenchain <wizbob@att.net>
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.
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
aug.lars.
data(longley2)
form <- GNP~GNP.deflator+Unemployed+Armed.Forces+Population+Year+Employed
rxucobj <- uc.lars(form, data=longley2)
rxucobj
plot(rxucobj)
str(rxucobj)
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