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Title: | A Taxonomy of Mixing and Outcome Distributions Based on Conjugacy and Bridging | Authors: | Kenward, Michael G. MOLENBERGHS, Geert |
Issue Date: | 2016 | Source: | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 45 (7), pag. 1953-1968 | Abstract: | The generalized linear mixed model is commonly used for the analysis of hierarchical non-Gaussian data. It combines an exponential family model formulation with normally distributed random effects. A drawback is the difficulty of deriving convenient marginal mean functions with straightforward parametric interpretations. Several solutions have been proposed, including the marginalized multilevel model (directly formulating the marginal mean, together with a hierarchical association structure) and the bridging approach (choosing the random-effects distribution such that marginal and hierarchical mean functions share functional forms). Another approach, useful in both a Bayesian and a maximum likelihood setting, is to choose a random-effects distribution that is conjugate to the outcome distribution. In this paper, we contrast the bridging and conjugate approaches. For binary outcomes, using characteristic functions and cumulant generating functions, it is shown that the bridge distribution is unique. Self-bridging is introduced as the situation in which the outcome and random-effects distributions are the same. It is shown that only the Gaussian and degenerate distributions have well-defined cumulant generating functions for which self-bridging holds. | Notes: | Molenberghs, G (reprint author), Univ Hasselt, I BioStat, Martelarenlaan 42, B-3500 Hasselt, Belgium. geert.molenberghs@uhasselt.be | Keywords: | cauchy distribution; characteristic function; cumulant; degenerate distribution; identity Link; logit link; log link; marginalization; mixed models; mixture distribution; probit link; random effects; random-effects distribution. | Document URI: | http://hdl.handle.net/1942/16505 | ISSN: | 0361-0926 | e-ISSN: | 1532-415X | DOI: | 10.1080/03610926.2013.870205 | ISI #: | 000372828900009 | Rights: | © 2016 Taylor & Francis Group, LLC | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2017 |
Appears in Collections: | Research publications |
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bridgetaxonomy04.pdf | Peer-reviewed author version | 171.38 kB | Adobe PDF | View/Open |
kenward2016.pdf Restricted Access | Published version | 684.26 kB | Adobe PDF | View/Open Request a copy |
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