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Hierarchical models with normal and conjugate random effects: a review (invited article)

    1. [1] University of Hasselt

      University of Hasselt

      Arrondissement Hasselt, Bélgica

    2. [2] Universidade de São Paulo

      Universidade de São Paulo

      Brasil

  • Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 41, Nº. 2, 2017, págs. 191-254
  • Idioma: inglés
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  • Resumen
    • Molenberghs, Verbeke, and Demétrio (2007) and Molenberghs et al. (2010) proposed a general framework to model hierarchical data subject to within-unit correlation and/or overdispersion. The framework extends classical overdispersion models as well as generalized linear mixed models. Subsequent work has examined various aspects that lead to the formulation of several extensions. A unified treatment of the model framework and key extensions is provided. Particular extensions discussed are: explicit calculation of correlation and other moment-based functions, joint modelling of several hierarchical sequences, versions with direct marginally interpretable parameters, zero-inflation in the count case, and influence diagnostics. The basic models and several extensions are illustrated using a set of key examples, one per data type (count, binary, multinomial, ordinal, and time-to-event).


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