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.
aug.lars(form, data, rscale = 1, type = "lar", trace = FALSE,
eps = .Machine$double.eps, omdmin = 9.9e-13)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 aug.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.)
An output list object of class aug.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-Ratio).
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 qm.ridge() and unr.ridge() are also computed and (optionally) plotted.
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.
Efron B, Hastie T. (2005) Least Angle Regression, Lasso and Forward Stagewise. https://CRAN.R-project.org/package=lars
Obenchain RL. (2005) Shrinkage Regression: ridge, BLUP, Bayes, spline and Stein. Electronic book-in-progress (185 pages.) http://localcontrolstatistics.org
Obenchain RL. (2020) RXshrink_in_R.PDF RXshrink package vignette-like file. http://localcontrolstatistics.org
Tibshirani R. (1996) Regression shrinkage and selection via the lasso. J. Roy. Stat. Soc. B 58, 267-288.
# NOT RUN {
data(longley2)
form <- GNP~GNP.deflator+Unemployed+Armed.Forces+Population+Year+Employed
rxlobj <- aug.lars(form, data=longley2)
rxlobj
plot(rxlobj)
str(rxlobj)
# }
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