Local Influence in Generalized Estimating Equations

Abstract

We investigate the influence of subjects or observations on regression coefficients of generalized estimating equations (GEEs) using local influence. The GEE approach does not require the full multivariate distribution of the response vector. We extend the likelihood displacement to a quasi-likelihood displacement, and propose local influence diagnostics under several perturbation schemes. An illustrative example in GEEs is given and we compare the results using the local influence and deletion methods. Copyright (c) Board of the Foundation of the Scandinavian Journal of Statistics 2007.

Approximate subject-deletion influence diagnostics for Inverse Probability of Censoring Weighted (IPCW) method

“…Even in the case of the independent working correlation, the formula is quite complicated and the arguments used in its derivation seem difficult to apply the case of general working correlation. Jung (2008) used a perturbation method to construct local influence measures with quasi-likelihood displacement for the GEE (without modeling of dropout under MCAR). However, it seems difficult to obtain a closed-form expression as (6) even for the GEE unless independent working correlation is employed.…”

Local Influence Analysis for Quasi-Likelihood Nonlinear Models with Random Effects

“…For the sake of coping with those difficulties, some authors have considered alternatives to replace LD( ). For instance, Zhu et al proposed in [25] the Q-likelihood displacement and established an approach to assess local influence of statistical models with incomplete data, and Jung presented in [26] a quasi-likelihood displacement to obtain local influence analysis in generalized estimating equations. Inspired by [25,26], we define in this work a new penalized quasi-likelihood displacement and then adapt the local influence approach introduced by [9] to the QLNMWRE.…”

“…Following the approach developed in [9,25,26], the normal curvature l of ( ) at 0 in the direction of some unit vector l can be used to summarize the local behavior of the penalized quasi-likelihood displacement. As shown in [9], the normal curvature l in the unit direction l(‖l‖ = 1) at 0 is given by…”

A power series beta Weibull regression model for predicting breast carcinoma

“…Here, is a (p+4)×n matrix, which depends on the perturbation scheme and whose elements are given by Δ ji = 2 l( | )∕ j i (i = 1, … , n and j = 1, … , p + 4) evaluated at̂and 0 , where 0 is the no perturbation vector (see [19,32,33]). For the PSBW model with long-term survivors, we calculate the normal curvatures C ( ) and C ( ) to perform various index plots, for instance, the index plot of the eigenvector max corresponding to the largest eigenvalue C , where {( k , k )|k = 1, … , n} are the eigenvalue-eigenvector pairs of with 1 ⩾ · · · ⩾ n 1 ⩾ n 1 +1 = · · · = n = 0, and { k = (e k1 , … , e kn ) T } is the associated orthonormal basis.…”