RXpredict {RXshrink}

Predictions from Models fit using RXshrink Generalized Ridge Estimation Methods.

Description

RXpredict() makes in-sample predictions (i.e. computes "fitted.values") for all 6 forms of RXshrink estimation either at some user-specified m-Extent of Shrinkage, such as m=0.963, or at the Normal distribution-theory m-Extent most likely to achieve minimum Risk (minMSE).

Usage

  RXpredict(x, data, m="minMSE", rscale=1)

Arguments

x

An object output by one of the 6 RXshrink estimation functions. Thus class(x) must be "qm.ridge", "eff.ridge", "aug.lars", "uc.lars", "MLcalc" or "correct.signs".

data

Existing data.frame containing observations on all variables used by the RXshrink function for estimation of regression coefficients.

m

The m argument can be either [i] a single "numeric" value that is non-negative and does not exceed rank(X) or [ii] the (default) string "minMSE" to request use of the observed m-Extent of shrinkage most likely to be MSE optimal under Normal distribution-theory. For example, m="0.0" requests use of the (unbaised) OLS estimate [BLUE].

rscale

One of two possible choices (0 or 1) for "rescaling" of variables (after being "centered") to remove all "non-essential" ill-conditioning. Use "rscale=0" only when the RXshrink estimation function that computed the x-object also used "rscale=0". The default of "rscale=1" should be used in all other cases.

Value

An output list object of class RXpredict:

cryprd

Predicted values for the "centered" and POSSIBLY "rescaled" outcome y-vector, cry. These values correspond, for example, to the default "predicted.values" from lm().

cry

This the "centered" and POSSIBLY "rescaled" outcome y-vector from the input data.frame.

yvecprd

Predicted values for the Y-outcome variable, yvec.

yvec

The Y-outcome vector from the input data.frame specified by the "data" argument.

m

"numeric" Value of m-Extent implied by the call to RXpredict(), possibly via a default call with m="minMSE". Restriction: 0 <= m <= rank(X).

mobs

Observed m-Extent most close to the requested m-Extent AND is on the lattice of observed m-Extents stored within the given x-object.

Author(s)

Bob Obenchain <[e-mail]>

References

Obenchain RL. (1978) Good and Optimal Ridge Estimators. Annals of Statistics 6, 1111-1121. doi:10.1214/aos/1176344314

Obenchain RL. (2005) Shrinkage Regression: ridge, BLUP, Bayes, spline and Stein. Electronic book-in-progress (185+ pages.) http://localcontrolstatistics.org

Obenchain RL. (2022) RXshrink_in_R.PDF RXshrink package vignette-like document, Version 2.2. http://localcontrolstatistics.org

See Also

qm.ridge, eff.ridge and MLtrue.

Examples

  data(tycobb)
  form <- batavg~atbats+seasons+CMspl
  rxefobj <- eff.ridge(form, data=tycobb)
  tycfit <- RXpredict(rxefobj, tycobb, m="minMSE")
  plot(tycfit)
  tycobb$batavg[18]  # Ty Cobb's batavg = 0.401 in 1922
  abline(h=tycfit$cry[18], lty=2, lwd=3, col="red")