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

• Geert Molenberghs ^[1] ; Geert Verbeke ^[1] ; Clarice G.B. Demétrio ^[2]
  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
• Enlaces
  • Texto completo (pdf)
• 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).