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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/12321

Title: A note on a hierarchical interpretation for negative variance components
Authors: Molenberghs, Geert
Verbeke, Geert
Issue Date: 2011
Citation: STATISTICAL MODELLING, 11(5). p. 389-408
Abstract: A lot has been said about the relationship between hierarchical models, such as linear mixed-effects models, and the marginal models they imply. Generally, there is a many-to-one map of hierarchical models onto a given marginal model. Additionally, in some cases, no obvious hierarchical model leads to a given marginal model. For example, it is commonly known that the random-intercepts model produces, marginally, a compound-symmetry model with non-negative intraclass correlation, whereas, on the other hand, a compound-symmetry model with negative intraclass correlation is not induced by a conventional random-intercepts model. We show here that it is still possible, and even intuitively appealing, to formulate hierarchical models inducing structure such as negative compound-symmetry correlation. Thus, the aim of this note is to further clarify the relationship between hierarchical and marginal models, enhancing appeal and establishing symmetry of the concepts. Consequences for interpretation and sensitivity analysis are discussed. The ideas are illustrated in three sets of data.
Notes: [Molenberghs, G] Univ Hasselt, Interuniv Inst Biostat & Stat Bioinformat, B-3590 Diepenbeek, Belgium. Katholieke Univ Leuven, Louvain, Belgium.
URI: http://hdl.handle.net/1942/12321
DOI: 10.1177/1471082X1001100501
ISI #: 000295840600001
ISSN: 1471-082X
Category: A1
Type: Journal Contribution
Validation: ecoom, 2012
Appears in Collections: Research publications

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