The functions in this package augment basic calculations of Generalized Ridge and Least Angle Regression with important visualization tools. Specifically, they display TRACEs of (biased) estimates for 5 KEY quantities [fitted coefficients, relative MSE, excess eigenvalues, inferior direction cosines and shrinkage factors] that completely characterize the effects of shrinkage along Paths with 2 or more parameters: (m-Extent plus q-Shape or Unrestricted). All Paths start at the Ordinary Least-Squares estimate [m = 0] and end at the origin, (0, 0, ..., 0), where all coefficient estimates have been shrunken to zero [m = p = rank(X).] Three different types of Likelihood of minimal MSE risk (Classical Normal-Theory, Empirical Bayes, and Random Coefficients) can be monitored to suggest an optimal m-Extent of shrinkage for the given matrix of X-variables and the observed y-outcome vector.
| Package: | RXshrink |
| Type: | Package |
| Version: | 1.4.3 |
| Date: | 2020-11-01 |
| License: | GNU GENERAL PUBLIC LICENSE, Version 2, June 1991 |
unr.ridge() calculates and displays TRACEs for an Unrestricted (p-parameter) shrinkage Path that always passes through the Beta coefficient point-estimate that is most likely to achieve optimal MSE risk reductions under Normal distribution-theory.
MLboot(), MLcalc() and MLhist() support use of Bootstrap resampling to study the bias and MSE risk characeristics of non-linear (unrestricted) Generalized Ridge Regression (GRR) estimators.
When true regression parameters have user-specified (KNOWN) numerical values, MLtrue() uses this information and generates a new data.frame that contains a y-outcome vector of the expected form with "disturbance" terms that are IID Normal errors-in-measurement. Arguments to MLtrue() must include the "formula" for a desired linear model and a data.frame containing the specified X-variables.
qm.ridge() calculates and displays TRACEs for traditional Paths defined by 2-parameters: q-Shape and m-Extent of Shrinkage. The restricted Path of most likely q-Shape is found via search on a lattice of 21 values within [-5,+5]. Default lattices for both q and m searches are easy to modify using the qmax, qmin, nq and steps arguments to qm.ridge(). The "ordinary" ridge Path of Hoerl and Kennard has q-Shape = 0, while "uniform" shrinkage corresponds to q-Shape = +1. None of these qm-Paths generally achieve overall minimum MSE risk when p > 2 because they restrict attention to Shrinkage-factors that are "monotome" (increasing or decreasing).
aug.lars() augments the Efron-Hastie lars() R-function to perform Least Angle Regression with MSE risk calculations and Maximum Likelihood TRACE displays ...like those of qm.ridge() and unr.ridge().
uc.lars() applies Least Angle Regression methods to the Uncorrelated Components of a possibly ill-conditioned set of x-variables. Calculations use a closed-form expression for lars/lasso shrinkage delta-factors that apply because NO Ill-Conditioning is present in these "uc" cases.
correct.signs() displays the Normal-theory maximum likelihood estimate of the regression coefficient vector that minimizes MSE Risk in the UNKNOWN direction of p-space PARALLEL to the true Beta vector. This estimate corrects "wrong-sign" problems in the sense that its coefficients have the same relative magnitudes and numerical signs as those of the "Correlation Form" of the X'y vector.
RXpredict() makes predictions (i.e. computes "fitted.values") for all 6 types of RXshrink estimation ...either at a user-specified m-Extent of Shrinkage or at the Normal-theory "minMSE" m-Extent.
Efron B, Hastie T, Johnstone I, Tibshirani R. (2003) Least angle regression. Annals of Statistics 32, 407-499.
Goldstein M, Smith AFM. (1974) Ridge-type estimators for regression analysis. J. Roy. Stat. Soc. B 36, 284-291. (The 2-parameter shrinkage family.)
Obenchain RL. (1975) Ridge Analysis Following a Preliminary Test of the Shrunken Hypothesis. Technometrics 17, 431-441. <doi:10.1080/00401706.1975.10489369>
Obenchain RL. (1978) Good and Optimal Ridge Estimators. Annals of Statistics 6, 1111-1121. <doi:10.1214/aos/1176344314>
Obenchain RL. (2020) Ridge TRACE Diagnostics. https://arxiv.org/abs/2005.14291
Obenchain RL. (2020) RXshrink_in_R.PDF RXshrink package vignette-like document. http://localcontrolstatistics.org
# NOT RUN {
demo(longley2)
# }
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