Please use this identifier to cite or link to this item:
http://hdl.handle.net/1942/13954
Title: | A combined beta and normal random-effects model for repeated, overdispersed binary and binomial data | Authors: | MOLENBERGHS, Geert VERBEKE, Geert IDDI, Samuel DEMETRIO, Clarice |
Issue Date: | 2012 | Publisher: | ELSEVIER INC | Source: | JOURNAL OF MULTIVARIATE ANALYSIS, 111, p. 94-109 | Abstract: | Non-Gaussian outcomes are often modeled using members of the so-called exponential family. Notorious members are the Bernoulli model for binary data, leading to logistic regression, and the Poisson model for count data, leading to Poisson regression. Two of the main reasons for extending this family are (1) the occurrence of overdispersion, meaning that the variability in the data is not adequately described by the models, which often exhibit a prescribed mean-variance link, and (2) the accommodation of hierarchical structure in the data, stemming from clustering in the data which, in turn, may result from repeatedly measuring the outcome, for various members of the same family, etc. The first issue is dealt with through a variety of overdispersion models, such as, for example, the beta-binomial model for grouped binary data and the negative-binomial model for counts. Clustering is often accommodated through the inclusion of random subject-specific effects. Though not always, one conventionally assumes such random effects to be normally distributed. While both of these phenomena may occur simultaneously, models combining them are uncommon. This paper starts from the broad class of generalized linear models accommodating overdispersion and clustering through two separate sets of random effects. We place particular emphasis on so-called conjugate random effects at the level of the mean for the first aspect and normal random effects embedded within the linear predictor for the second aspect, even though our family is more general. The binary and binomial cases are our focus. Apart from model formulation, we present an overview of estimation methods, and then settle for maximum likelihood estimation with analytic-numerical integration. The methodology is applied to two datasets of which the outcomes are binary and binomial, respectively. (C) 2012 Elsevier Inc. All rights reserved. | Notes: | [Molenberghs, Geert; Verbeke, Geert; Iddi, Samuel] Univ Hasselt, Ctr Stat, B-3590 Diepenbeek, Belgium. [Molenberghs, Geert; Verbeke, Geert; Iddi, Samuel] Katholieke Univ Leuven, Ctr Biostat, B-3000 Louvain, Belgium. [Demetrio, Clarice G. B.] ESALQ, Sao Paulo, Brazil. geert.molenberghs@uhasselt.be | Keywords: | statistics & probability; Bernoulli model; binomial model; beta-binomial model; conjugacy; logistic-normal model; maximum likelihood; strong conjugacy;Bernoulli model; Binomial model; Beta-binomial model; Conjugacy; Logistic-normal model; Maximum likelihood; Strong conjugacy | Document URI: | http://hdl.handle.net/1942/13954 | ISSN: | 0047-259X | DOI: | 10.1016/j.jmva.2012.05.005 | ISI #: | 000306767400007 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2013 |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
overdispersionbinary05.pdf | Peer-reviewed author version | 466.55 kB | Adobe PDF | View/Open |
molenberghs 1.pdf Restricted Access | Published version | 608.7 kB | Adobe PDF | View/Open Request a copy |
SCOPUSTM
Citations
10
checked on Sep 2, 2020
WEB OF SCIENCETM
Citations
19
checked on Oct 14, 2024
Page view(s)
118
checked on Sep 6, 2022
Download(s)
180
checked on Sep 6, 2022
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.