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R: True MSE Risk of Shrinkage Resulting from Known Regression...

RXtrisk

R Documentation

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.
`Q`	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.)

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.

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.
`qp`	Numerical value of the Q-shape actually used for shrinkage.
`p`	Number of regression predictor variables.
`n`	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.

Author(s)

Bob Obenchain <wizbob@att.net>

Examples

  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)

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(RXshrink)
Loading required package: lars
Loaded lars 1.2

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/RXshrink/RXtrisk.Rd_%03d_medium.png", width=480, height=480)
> ### Name: RXtrisk
> ### Title: True MSE Risk of Shrinkage Resulting from Known Regression
> ###   Parameters
> ### Aliases: RXtrisk
> ### Keywords: regression hplot
> 
> ### ** Examples
> 
>   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)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>