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

Prior weights and offsets are supported: the score is evaluated in the same prior-weight-whitened coordinates the estimator iterates in (U_e = \mathrm{diag}(\sqrt{w}), residuals offset-corrected).

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 July 30, 2026, 5:11 p.m.