TY - DATA
T1 - A taxonomy of mixing and outcome distributions based on conjugacy and bridging
PY - 2016/03/16
AU - Michael G. Kenward
AU - Geert Molenberghs
UR - https://figshare.com/articles/A_taxonomy_of_mixing_and_outcome_distributions_based_on_conjugacy_and_bridging/3115558
DO - 10.6084/m9.figshare.3115558.v1
L4 - https://ndownloader.figshare.com/files/4843453
KW - Cauchy distribution
KW - Characteristic function
KW - Cumulant
KW - Degenerate distribution
KW - Identity link
KW - Logit link
KW - Log link
KW - Marginalization
KW - Mixed models
KW - Mixture distribution
KW - Probit link
KW - Random effects
KW - Random-effects distribution
KW - 62F99
KW - 62P10
N2 - The generalized linear mixed model (GLMM) is commonly used for the analysis of hierarchical non Gaussian data. It combines an exponential family model formulation with normally distributed random effects. A drawback is the difficulty of deriving convenient marginal mean functions with straightforward parametric interpretations. Several solutions have been proposed, including the marginalized multilevel model (directly formulating the marginal mean, together with a hierarchical association structure) and the bridging approach (choosing the random-effects distribution such that marginal and hierarchical mean functions share functional forms). Another approach, useful in both a Bayesian and a maximum-likelihood setting, is to choose a random-effects distribution that is conjugate to the outcome distribution. In this paper, we contrast the bridging and conjugate approaches. For binary outcomes, using characteristic functions and cumulant generating functions, it is shown that the bridge distribution is unique. Self-bridging is introduced as the situation in which the outcome and random-effects distributions are the same. It is shown that only the Gaussian and degenerate distributions have well-defined cumulant generating functions for which self-bridging holds.
ER -