Reference Bayesian Methods for Generalized Linear Mixed Models

By R. Natarajan, Robert E. Kass. 2000

238 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d3eb08cab8492a14b6c2e8cb081173e40c2c9cd8

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Citations in the corpus

Bivariate Binomial Spatial Modeling of Loa loa Prevalence in Tropical Africa (2008, methodology): “Alternatives to gamma priors have been discussed by, for example, Natarajan and Kass (2000) and Gelman (2006).”
Modeling Differential Item Functioning Using a Generalization of the Multiple-Group Bifactor Model (2013, background): “However, these techniques tend to be slow, and it is difficult to monitor convergence to a stationary distribution and to specify vague priors for variance parameters (e.g., Browne & Draper, 2006; Natarajan & Kass, 2000).”
A Bayesian Approach for Estimating Multilevel Latent Contextual Models (2016, background): “…it is often less critical to select priors for regression coefficients, there is an ongoing discussion about which prior distribution should be specified for variance components (e.g., Browne & Draper, 2006; Chung, Rabe-Hesketh, Dorie, Gelman, & Liu, 2013; Gelman, 2006; Natarajan & Kass, 2000).”
Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) (2004, methodology): “Specifying a prior distribution jointly on variance components at different levels of the model could be seen as a generalization of priors on the shrinkage factor, which is a function of both σy and σα (see Daniels, 1999, Natarajan and Kass, 2000, and Spiegelhalter, Abrams, and Myles, 2004, for an ”
Spatially Adaptive Bayesian Penalized Splines With Heteroscedastic Errors (2007, unknown): “Alternative to gamma priors are discussed by, for example, Natarajan and Kass (2000) and Gelman (2006).”
How vague is vague? A simulation study of the impact of the use of vague prior distributions in MCMC using WinBUGS (2005, methodology): “A further approach to the choice of prior distribution is to use uniform shrinkage priors [10, 39, 40].”
Bayesian measures of model complexity and fit (2002, background): “Natarajan and Kass (2000) have pointed out potential problems with the gamma(0.001,0.001) prior on λ, but in this context the 537 random effects ensure that these findings are robust to the choice of prior for λ.”
brms: An R Package for Bayesian Multilevel Models Using Stan (2017, background): “However, there are good arguments against the Inverse-Wishart prior (Natarajan and Kass 2000; Kass and Natarajan 2006).”
Conservative prior distributions for variance parameters in hierarchical models (2006, methodology): “As discussed by Natarajan and Kass (2000), this sort of argument leads to a data-dependent prior distribution.”
A default conjugate prior for variance components in generalized linear mixed models (comment on article by Browne and Draper) (2006, methodology): “The conditions under which this gives a proper posterior for GLMMs has been derived by Natarajan and Kass (2000), and were verified for the data here. Inferences for the four priors were based on 2,000 samples generated from their posterior distributions for each data set. Posterior sampling was per”
Small area estimation of general parameters with application to poverty indicators: A hierarchical Bayes approach (2014, unknown): “By Bayes’ theorem, the posterior density of µ is µ|Y ∼N{ρY + (1− ρ)θ, ρσ2}, which leads to the shrinkage or reference prior for ρ given by ρ ∼ U(0,1); see Natarajan and Kass (2000).”
Multilevel Modeling with Correlated Effects (2007, background): “First, one must specify priors at each model level, and the choice of priors can influence inference results (Natarajan and Kass, 2000).”