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Title: Marginalized multilevel hurdle and zero-inflated models for overdispersed and correlated count data with excess zeros
Authors: Kassahun, Wondwosen 
Neyens, Thomas 
Molenberghs, Geert 
Faes, Christel 
Verbeke, Geert 
Issue Date: 2014
Source: STATISTICS IN MEDICINE, 33 (25), p. 4402-4419
Abstract: Count data are collected repeatedly over time in many applications, such as biology, epidemiology, and public health. Such data are often characterized by the following three features. First, correlation due to the repeated measures is usually accounted for using subject-specific random effects, which are assumed to be normally distributed. Second, the sample variance may exceed the mean, and hence, the theoretical mean-variance relationship is violated, leading to overdispersion. This is usually allowed for based on a hierarchical approach, combining a Poisson model with gamma distributed random effects. Third, an excess of zeros beyond what standard count distributions can predict is often handled by either the hurdle or the zero-inflated model. A zero-inflated model assumes two processes as sources of zeros and combines a count distribution with a discrete point mass as a mixture, while the hurdle model separately handles zero observations and positive counts, where then a truncated-at-zero count distribution is used for the non-zero state. In practice, however, all these three features can appear simultaneously. Hence, a modeling framework that incorporates all three is necessary, and this presents challenges for the data analysis. Such models, when conditionally specified, will naturally have a subject-specific interpretation. However, adopting their purposefully modified marginalized versions leads to a direct marginal or population-averaged interpretation for parameter estimates of covariate effects, which is the primary interest in many applications. In this paper, we present a marginalized hurdle model and a marginalized zero-inflated model for correlated and overdispersed count data with excess zero observations and then illustrate these further with two case studies. The first dataset focuses on the Anopheles mosquito density around a hydroelectric dam, while adolescents' involvement in work, to earn money and support their families or themselves, is studied in the second example. Sub-models, which result from omitting zero-inflation and/or overdispersion features, are also considered for comparison's purpose. Analysis of the two datasets showed that accounting for the correlation, overdispersion, and excess zeros simultaneously resulted in a better fit to the data and, more importantly, that omission of any of them leads to incorrect marginal inference and erroneous conclusions about covariate effects. Copyright (c) 2014 John Wiley & Sons, Ltd.
Notes: [Kassahun, Wondwosen] Jimma Univ, Dept Epidemiol & Biostat, Jimma, Ethiopia. [Neyens, Thomas; Molenberghs, Geert; Faes, Christel; Verbeke, Geert] Univ Hasselt, B-3590 Diepenbeek, Belgium. [Molenberghs, Geert; Verbeke, Geert] Katholieke Univ Leuven, B-3000 Leuven, Belgium.
Keywords: clustering; hurdle model; marginal model; multilevel model; overdispersion; zero-inflated model;clustering; hurdle model; marginal model; multilevel model; overdispersion; zero-inflated model
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ISSN: 0277-6715
e-ISSN: 1097-0258
DOI: 10.1002/sim.6237
ISI #: 000342898500006
Rights: Copyright © 2014 John Wiley & Sons, Ltd.
Category: A1
Type: Journal Contribution
Validations: ecoom 2015
Appears in Collections:Research publications

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