RXuclars {RXshrink}R Documentation

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

  RXuclars(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 to the lars() function in the lars R-package.

Details

RXuclars() 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 RXuclars:

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

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

Obenchain RL. (1994-2005) Shrinkage Regression: ridge, BLUP, Bayes, spline and Stein. members.iquest.net/~softrx.

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

See Also

RXlarlso.

Examples

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

[Package RXshrink version 1.0-4 Index]