ransac_basin_radius: Redescender basin (support-preservation) radius

In robustlmm: Robust Linear Mixed Effects Models

Redescender basin (support-preservation) radius

Description

Support-preservation (basin) radius for a fixed-effects start.

Usage

ransac_basin_radius(object, cc = NULL, rho = NULL)

Arguments

object	a fitted lmerMod or rlmerMod supplying the error scale \sigma and the fixed-effects design matrix.
cc	the rejection point c of the redescender. If NULL and rho is supplied, c is the rejection point of rho found numerically; if both are NULL, the bisquare default 4.685.
rho	an optional redescending psi_func_rcpp (e.g. bisquarePsi, lqqPsi) whose rejection point supplies c when cc is NULL.

Details

Computes the radius r^\star(c) = c\,\sigma / (2 \max_j \|x_j\|) of the ball around the initial fixed-effects estimate within which every observation keeps its redescender-support membership, so the population Hessian stays positive definite (Koller and Stahel; the RANSAC-RSE basin theorem). Here c is the rejection point of the redescending \psi — the smallest x > 0 with \psi(x) = 0. For the bisquare this is the tuning cutoff (default 4.685); the geometry generalises to any finite-rejection-point redescender (e.g. lqqPsi) by finding its rejection point numerically. A redescending \psi is safe to engage from a start only if the eventual estimate stays within this radius of the (high-breakdown) start — otherwise the iteration may leave the basin and converge to a phony solution.

Value

the basin radius r^\star(c) in the units of \beta (a scalar), with attribute "max_xnorm".

robustlmm documentation built on July 30, 2026, 5:11 p.m.