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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/22669

Title: Local Influence Diagnostics for Generalized Linear Mixed Models With Overdispersion
Authors: Rakhmawati, Trias Wahyuni
Molenberghs, Geert
Verbeke, Geert
Faes, Christel
Issue Date: 2016
Citation: JOURNAL OF APPLIED STATISTICS, 44 (4), pag. 620-641
Abstract: Since the seminal paper by Cook and Weisberg [9 R.D. Cook and S. Weisberg, Residuals and Influence in Regression, Chapman & Hall, London, 1982.], 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 E. Lesaffre and G. Verbeke, Local influence in linear mixed models, Biometrics 54 (1998), pp. 570–582. doi: 10.2307/3109764 [CrossRef], [PubMed], [Web of Science ®]. Ouwens et al. [24 M.J.N.M. Ouwens, F.E.S. Tan, and M.P.F. Berger, Local influence to detect influential data structures for generalized linear mixed models, Biometrics 57 (2001), pp. 1166–1172. doi: 10.1111/j.0006-341X.2001.01166.x [CrossRef], [PubMed], [Web of Science ®] 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.
Notes: Rakhmawati, TW (reprint author), Univ Hasselt, I BioStat, B-3500 Hasselt, Belgium. triaswahyuni.rakhmawati@uhasselt.be
URI: http://hdl.handle.net/1942/22669
DOI: 10.1080/02664763.2016.1182128
ISI #: 000396038500004
ISSN: 0266-4763
Category: A1
Type: Journal Contribution
Appears in Collections: Research publications

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