Case-deletion measures for models with incomplete data

Zhu, Hongtu; Lee, Sik‐Yum; Wei, Bo‐Cheng; Zhou, Julie

doi:10.1093/biomet/88.3.727

Cited by 79 publications

(58 citation statements)

References 8 publications

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“…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.…”

Section: Standard Approachmentioning

confidence: 99%

Local influence diagnostics for incomplete overdispersed longitudinal counts

Rakhmawati

Molenberghs

Verbeke

et al. 2016

Journal of Applied Statistics

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Since the seminal paper by Cook and Weisberg [9], local influence, next to case deletion, has gained popularity as a tool to detect influential subjects and measurements for a variety of statistical models. For the linear mixed model the approach leads to easily interpretable and computationally convenient expressions, not only highlighting influential subjects, but also which aspect of their profile leads to undue influence on the model's fit [17]. Ouwens et al. [24] applied the method to the Poisson-normal generalized linear mixed model (GLMM). Given the model's nonlinear structure, these authors did not derive interpretable components but rather focused on a graphical depiction of influence. In this paper, we consider GLMMs for binary, count, and time-to-event data, with the additional feature of accommodating overdispersion whenever necessary. For each situation, three approaches are considered, based on: (1) purely numerical derivations; (2) using a closed-form expression of the marginal likelihood function; and (3) using an integral representation of this likelihood. Unlike when case deletion is used, this leads to interpretable components, allowing not only to identify influential subjects, but also to study the cause thereof. The methodology is illustrated in case studies that range over the three data types mentioned. ARTICLE HISTORY

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Section: Standard Approachmentioning

confidence: 99%

Local influence diagnostics for incomplete overdispersed longitudinal counts

Rakhmawati

Molenberghs

Verbeke

et al. 2016

Journal of Applied Statistics

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“…Also, similar to the definition of likelihood displacement, [18] we define Q-function-based displacement as…”

Section: Case-deletion Diagnosticsmentioning

confidence: 99%

“…The case-deletion method [15] is usually adopted to quantify the impact of individuals on parameter estimates or quantities of interest, and has been successfully applied to various models including linear regression models, [15] linear mixed models, [16] exponential family nonlinear models [17] and incomplete data models. [18] Local influence analysis [19] is often used to assess the model sensibility under some minor perturbations and has been extended to various models such as linear mixed models, [20] incomplete data model, [21] generalized linear models, [22] nonlinear structural equation models [23] and generalized linear mixed models. [24] However, there is little work done on diagnostic analysis for SNRDMMs via the case-deletion method and local influence approach.…”

Section: Introductionmentioning

confidence: 99%

Maximum-likelihood estimation and influence analysis in multivariate skew-normal reproductive dispersion mixed models for longitudinal data

Zhao

Tang

2015

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Various mixed models were developed to capture the features of between-and within-individual variation for longitudinal data under the normality assumption of the random effect and the within-individual random error. However, the normality assumption may be violated in some applications. To this end, this article assumes that the random effect follows a skew-normal distribution and the within-individual error is distributed as a reproductive dispersion model. An expectation conditional maximization (ECME) algorithm together with the Metropolis-Hastings (MH) algorithm within the Gibbs sampler is presented to simultaneously obtain estimates of parameters and random effects. Several diagnostic measures are developed to identify the potentially influential cases and assess the effect of minor perturbation to model assumptions via the case-deletion method and local influence analysis. To reduce the computational burden, we derive the first-order approximations to case-deletion diagnostics. Several simulation studies and a real data example are presented to illustrate the newly developed methodologies.

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“…Since pioneering work of Cook (1977), case-deletion statistics, such as the Cook's distance and the likelihood distance have been successfully applied to various statistical models, see for example Andersen (1992), Banerjee and Frees (1997), Wei (1998), Zhu et al (2001Zhu et al ( , 2008, and references therein. However, seldom paper studied diagnostics about the fuzzy regression models.…”

Section: Introductionmentioning

confidence: 99%