implicitIF: Implicit (numerical) influence function building blocks for...

In robustlmm: Robust Linear Mixed Effects Models

Implicit (numerical) influence function building blocks for an rlmer fit.

Description

Computes the local-shift sensitivity \partial \hat{\beta}/\partial y (and the analogous quantity for the spherical random effects \hat{u}) by implicit differentiation of the joint (\beta, u)-scoring equations at the fit. The returned list is a building block for caseweightIF and vcov_sandwich; users who only want robust standard errors should call vcov(object, type = "sandwich").

Usage

implicitIF(fit, use.expected = FALSE)

Arguments

fit	An rlmerMod object.
use.expected	If TRUE, use E[\psi'] for the diagonal blocks of the Jacobian; the default (FALSE) uses the actual \psi' values at the fitted residuals (the empirical version).

Details

This is the partial (\sigma, \theta held fixed) version. It is not the Hampel influence function; the Hampel object is caseweightIF, which reuses the same Jacobian but with the score value \psi on the right-hand side rather than \partial_y \psi. See Koller (2026, Paper 1) for a discussion.

Value

A list with components IF_beta, IF_u, IF_b, the Jacobian blocks Jbb, Jbu, Jub, S, and intermediate rotated-design matrices used by the cluster sandwich. IF_beta is the local-shift sensitivity matrix p \times n.

robustlmm documentation built on June 21, 2026, 5:12 p.m.