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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/24102

Title: Negative variance components for non-negative hierarchical data with correlation, over-, and/or underdispersion
Authors: Oliveira, I. R. C.
Molenberghs, Geert
Verbeke, Geert
Demetrio, C. G. B.
Dias, C. T. S.
Issue Date: 2017
Citation: JOURNAL OF APPLIED STATISTICS, 44(6), p. 1047-1063
Abstract: The concept of negative variance components in linear mixed-effects models, while confusing at first sight, has received considerable attention in the literature, for well over half a century, following the early work of Chernoff[7] and Nelder[21]. Broadly, negative variance components in linear mixed models are allowable if inferences are restricted to the implied marginal model. When a hierarchical view-point is adopted, in the sense that outcomes are specified conditionally upon random effects, the variance-covariance matrix of the random effects must be positive-definite (positive-semi-definite is also possible, but raises issues of degenerate distributions). Many contemporary software packages allow for this distinction. Less work has been done for generalized linear mixed models. Here, we study such models, with extension to allow for overdispersion, for non-negative outcomes (counts). Using a study of trichomes counts on tomato plants, it is illustrated how such negative variance components play a natural role in modeling both the correlation between repeated measures on the same experimental unit and over- or underdispersion.
Notes: [Oliveira, I. R. C.; Demetrio, C. G. B.; Dias, C. T. S.] ESALQ, Dept Exact Sci, BR-13418900 Piracicaba, SP, Brazil. [Oliveira, I. R. C.; Molenberghs, G.] Univ Hasselt, Interuniv Inst Biostat & Stat Bioinformat, Hasselt, Belgium. [Molenberghs, G.; Verbeke, G.] Katholieke Univ Leuven, Interuniv Inst Biostat & Stat Bioinformat, Leuven, Belgium.
URI: http://hdl.handle.net/1942/24102
DOI: 10.1080/02664763.2016.1191624
ISI #: 000399325700007
ISSN: 0266-4763
Category: A1
Type: Journal Contribution
Appears in Collections: Research publications

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