RXlarlso {RXshrink}R Documentation

Maximum Likelihood Estimation of Effects in Least Angle Regression

Description

Identify whether least angle regression estimates are generalized ridge shrinkage estimates and generate TRACE displays for estimates that do correspond to ridge shrinkage factors between 0.00 and 0.99.

Usage

RXlarlso(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 as they are being "centered" to remove 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 RXlarlso() 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.)
... Optional argument(s) passed on to the lars() function from the lars R-package.

Details

RXlarlso() 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 RXridge are also computed and (optionally) plotted.

Value

An output list object of class RXlarlso:

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.
crlqstat Listing of criteria for maximum likelihood selection of path Q-shape.
qmse Numerical value of Q-shape most likely to be optimal.
qp Numerical value of the Q-shape actually used for shrinkage.
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.

Author(s)

Bob Obenchain <wizbob@att.net>

References

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

Efron B, Hastie T, Johnstone I, Tibshirani R. (2004) Least angle regression. Ann. Statis. 32, 407-499.

Obenchain RL. (2005) Shrinkage Regression: ridge, BLUP, Bayes, spline and Stein. Electronic book-in-progress (200+ pages.) http://members.iquest.net/~softrx/

Obenchain RL. (2009) RXshrink-R.PDF ../R_HOME/library/RXshrink

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

See Also

RXuclars.

Examples

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

[Package RXshrink version 1.0-4 Index]