RXtrisk: True MSE Risk of Shrinkage Resulting from Known Regression Parameters

Description

By specifying numerical values for regression parameters (uncorrelated components and error sigma) that usually are unknown, these functions can calculate and display True MSE Risk statistics associated with shrinkage along a given Q-shaped path.

Usage

RXtrisk(form, data, trug, trus, Q = 0, rscale = 1, steps = 8, qmax = 5, qmin = -5)

Arguments

form

A regression formula [y~x1+x2+...] suitable for use with lm().

data

Data frame containing observations on all variables in the formula.

trug

Column vector of numerical values for the true uncorrelated components of the regression coefficient vector.

trus

Numerical value for the true error standard deviation, Sigma.

Numerical value for the shape parameter controlling shrinkage path curvature. Default shape is Q = 0 for Hoerl-Kennard "ordinary" ridge regression.

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.

steps

Number of equally spaced values per unit change along the horizontal M-extent-of-shrinkage axis where estimates are calculated and displayed in TRACES (default = 8.)

qmax

Maximum allowed Q-shape (default = +5.)

qmin

Minimum allowed Q-shape (default = -5.)

Value

An output list object of class RXtrisk:

form

The regression formula specified as the first argument.

data

Name of the data.frame object specified as the second argument.

trug

Vector of numerical values for the true uncorrelated gamma components.

trus

Numerical value for the true error standard deviation, Sigma.

Numerical value of the Q-shape actually used for shrinkage.

Number of regression predictor variables.

Number of complete observations after removal of all missing values.

prinstat

Listing of principal statistics.

coef

Matrix of expected shrinkage-ridge regression coefficients.

rmse

Matrix of true MSE risk values for shrunken coefficients.

exev

Matrix of true excess eigenvalues (ordinary least squares minus ridge.)

infd

Matrix of direction cosines for the true inferior direction, if any.

spat

Matrix of shrinkage pattern delta factors.

sext

Listing of summary statistics for all M-extents-of-shrinkage.

Details

The RXridge() functions calculate maximum likelihood estimates (corrected, if necessary, so as to have correct range) for typical statistical inference situations where regression parameters are unknowns. In sharp contrast with this usual situation, the RXtrisk() functions show exactly how expected regression coefficients and true Mean Squared Error Risk actually do change with shrinkage when regression parameters take on specified, KNOWN numerical values.

Examples

Run this code

# NOT RUN {
  data(mpg)  
  form <- mpg~cylnds+cubins+hpower+weight
  rxrobj <- RXridge(form, data=mpg)
  # define true parameter values.
  trugam <- matrix(c(-.5,-.1,.1,-.6),4,1)
  trusig <- 0.4
  # create true shrinkage MSE risk scenario.
  trumse <- RXtrisk(form, data=mpg, trugam, trusig, Q=-1, steps=4)
  plot(trumse)
  str(trumse)
# }