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Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm
Summary. Two new implementations of the EM algorithm are proposed for maximum likelihood fitting of generalized linear mixed models. Both methods use random (independent and identically distributed)Expand
The Effect of Improper Priors on Gibbs Sampling in Hierarchical Linear Mixed Models
Abstract Often, either from a lack of prior information or simply for convenience, variance components are modeled with improper priors in hierarchical linear mixed models. Although the posteriorExpand
Standard Errors of Prediction in Generalized Linear Mixed Models
Abstract The unconditional mean squared error of prediction (UMSEP) is widely used as a measure of prediction variance for inferences concerning linear combinations of fixed and random effects in theExpand
On the applicability of regenerative simulation in Markov chain Monte Carlo
We consider the central limit theorem and the calculation of asymptotic standard errors for the ergodic averages constructed in Markov chain Monte Carlo. Chan & Geyer (1994) established a centralExpand
2. Random-Effects Modeling of Categorical Response Data
In many applications observations have some type of clustering, with observations within clusters tending to be correlated. A common instance of this occurs when each subject in the sample undergoesExpand
Honest Exploration of Intractable Probability Distributions via Markov Chain Monte Carlo
Two important questions that must be answered whenever a Markov chain Monte Carlo (MCMC) algorithm is used are (Q1) What is an appropriate burn-in? and (Q2) How long should the sampling continueExpand
A theoretical comparison of the data augmentation, marginal augmentation and PX-DA algorithms
The data augmentation (DA) algorithm is a widely used Markov chain Monte Carlo (MCMC) algorithm that is based on a Markov transition density of the form p(x|x') = fy f X|Y (x|y) f Y|X (y|x')dy, whereExpand
Negative binomial loglinear mixed models
The Poisson loglinear model is a common choice for explaining variability in counts. However, in many practical circumstances the restriction that the mean and variance are equal is not realistic.Expand
The Polya-Gamma Gibbs sampler for Bayesian logistic regression is uniformly ergodic
One of the most widely used data augmentation algorithms is Albert and Chib’s (1993) algorithm for Bayesian probit regression. Polson, Scott and Windle (2013) recently introduced an analogousExpand
Clustering using objective functions and stochastic search
A new approach to clustering multivariate data, based on a multilevel linear mixed model, is proposed. A key feature of the model is that observations from the same cluster are correlated, becauseExpand