robustlmm (version 3.5.0-2)

makeRobustbasePsi: Redescending psi-functions from robustbase (bisquare, lqq, optimal, hampel, ggw)

Description

Construct a redescending psi-function from one of robustbase's compiled Mpsi families.

Usage

makeRobustbasePsi(
  family = c("bisquare", "lqq", "optimal", "hampel", "ggw"),
  cc = NULL
)

Value

psi_func_rcpp object usable as rho.e (or rho.b,

rho.sigma.e, rho.sigma.b) in rlmer.

Arguments

family

robustbase Mpsi family name, one of "bisquare", "lqq", "optimal", "hampel", "ggw".

cc

tuning constant (a scalar for "bisquare" / "optimal", a specification vector for "lqq" / "ggw" / "hampel"). NULL uses the family's robustbase default (about 95% efficiency at the normal).

Details

Returns a psi_func_rcpp object whose psi, rho, weight and derivative slots delegate to robustbase's compiled psi-function family, so the shipped functions match lmrob exactly. The psi, its derivative and the weight are Mpsi(x, cc, family, 0), Mpsi(x, cc, family, 1) and Mwgt(x, cc, family); the rho slot is the normalised Mchi(x, cc, family) * MrhoInf(cc, family), so that rho(Inf) equals the supremum of rho (the psi_func rho convention used by rlmer). The Fisher consistency expectations (Erho, Epsi2, EDpsi) are computed by numerical integration against the standard normal.

The available families are the redescenders "bisquare" (Tukey biweight), "lqq" (linear-quadratic-quadratic), "optimal", "hampel" and "ggw" (generalised Gauss-weight). When cc is NULL the family's default tuning (\(\approx 95\%\) efficiency at the normal) is taken from robustbase::.Mpsi.tuning.default(family); for "lqq", "ggw" and "hampel" this is a short numeric specification vector rather than a single cutoff (see lmrob.control).

Of the redescenders, bisquarePsi redescends comparatively fast; the "lqq" psi of Koller and Stahel (2011), used by robustbase's lmrob.control(setting = "KS2014"), is the recommended redescender and is pre-built as lqqPsi.

References

Koller, M. and Stahel, W. A. (2011) Sharpening Wald-type inference in robust regression for small samples. Computational Statistics & Data Analysis 55(8), 2504--2515.

See Also

lqqPsi, bisquarePsi, Mpsi, lmrob.control.

Examples

  pf <- makeRobustbasePsi("lqq")
  pf@psi(c(-6, -3, 0, 3, 6))