RXshrink (version 1.0-5)

RXuclars: 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

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.

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.
• 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.

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.

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. (2010) RXshrink-R.PDF ../R_HOME/library/RXshrink/doc

See Also

RXlarlso.

Examples

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