Local Influence for Incomplete Data Models

Abstract

This paper proposes a method to assess the local in¯uence in a minor perturbation of a statistical model with incomplete data. The idea is to utilize Cook's approach to the conditional expectation of the complete-data log-likelihood function in the EM algorithm. It is shown that the method proposed produces analytic results that are very similar to those obtained from a classical local in¯uence approach based on the observed data likelihood function and has the potential to assess a variety of complicated models that cannot be handled by existing methods. An application to the generalized linear mixed model is investigated. Some illustrative arti®cial and real examples are presented.

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…”

Local influence diagnostics for incomplete overdispersed longitudinal counts

“…Zhu and Lee [30] and Zhu et al [31] proposed another approach to deal with the measurement of the distance betweenθ ω andθ . Instead of using the observed-data loglikelihood, their method is applied to the objective function that features in the expectation step of the EM algorithm.…”

Local influence for spatial analysis of soil physical properties and soybean yield using student's t-distribution

“…Due to the difficulty of its application to complicated models, Zhu & Lee (2001) proposed an option with a shift function for…”

“…Solo, 35:1917Solo, 35: -1926Solo, 35: , 2011 Given the matrix B fQ , l and considering Ci = 2*|b ii | (6) where b ii are the elements of the main diagonal of matrix B fQ , l , we find graph C i according to order i, to analyze the existence of influential observations in the spatial dependence structure. Zhu & Lee (2001) stated that for C i , the i th point is influential in the spatial dependence structure if:…”