A note on Influence diagnostics in nonlinear mixed-effects elliptical models

TL;DR

This paper derives general matrix formulas for influence diagnostics in nonlinear mixed-effects elliptical models, simplifying complex calculations and including formulas for score, Fisher information, and leverage.

Contribution

It introduces compact, general matrix formulas for influence diagnostics in a broad class of nonlinear mixed-effects elliptical models, extending previous work.

Findings

Provides explicit formulas for score and Fisher information matrices.

Includes derivation of generalized leverage expression.

Simplifies influence diagnostics calculations for complex models.

Abstract

This paper provides general matrix formulas for computing the score function, the (expected and observed) Fisher information and the $\Delta$ matrices (required for the assessment of local influence) for a quite general model which includes the one proposed by Russo et al. (2009). Additionally, we also present an expression for the generalized leverage. The matrix formulation has a considerable advantage, since although the complexity of the postulated model, all general formulas are compact, clear and have nice forms.