RXuclars {RXshrink} | R Documentation |
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.
RXuclars(form, data, rscale = 1, type = "lar", trace = FALSE, eps = .Machine$double.eps, omdmin = 9.9e-13, ...)
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. |
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.
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. |
Bob Obenchain <wizbob@att.net>
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
data(longley2) form <- GNP~GNP.deflator+Unemployed+Armed.Forces+Population+Year+Employed rxuobj <- RXuclars(form, data=longley2) rxuobj plot(rxuobj)