title: Influence analysis for linear mixed-effects models.
abstract: In this paper, we extend several regression diagnostic techniques commonly used in linear regression, such as leverage, infinitesimal influence, case deletion diagnostics, Cook's distance, and local influence to the linear mixed-effects model. In each case, the proposed new measure has a direct interpretation in terms of the effects on a parameter of interest, and collapses to the familiar linear regression measure when there are no random effects. The new measures are explicitly defined functions and do not necessitate re-estimation of the model, especially for cluster deletion diagnostics. The basis for both the cluster deletion diagnostics and Cook's distance is a generalization of Miller's simple update formula for case deletion for linear models. Pregibon's infinitesimal case deletion diagnostics is adapted to the linear mixed-effects model. A simple compact matrix formula is derived to assess the local influence of the fixed-effects regression coefficients. Finally, a link between the local influence approach and Cook's distance is established. These influence measures are applied to an analysis of 5-year Medicare reimbursements to colon cancer patients to identify the most influential observations and their effects on the fixed-effects coefficients.
authors.affiliation: Dartmouth Medical School, Hanover, NH 03755, USA. eugene.demidenko@dartmouth.edu
authors.forename: Eugene
authors.initials: E
authors.lastname: Demidenko
authors.forename: Therese A
authors.initials: TA
authors.lastname: Stukel
mesh_terms: D016000:Cluster Analysis; D003110:Colonic Neoplasms / Q000191:economics; D005260:Female; D006801:Humans; D016014:Linear Models; D008297:Male; D006278:Medicare / Q000191:economics; D018803:Models, Economic; D014481:United States