RXpredict function

Predictions from Models fit using RXshrink Generalized Ridge Estimation Methods.

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).

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.

Returns

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.

References

Obenchain RL. (1978) Good and Optimal Ridge Estimators. Annals of Statistics

6 , 1111-1121. tools:::Rd_expr_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

Author(s)

Bob Obenchain wizbob@att.net

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")