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11
Model Choice: A Minimum Posterior Predictive Loss Approach
, 1998
"... Model choice is a fundamental and much discussed activity in the analysis of data sets. Hierarchical models introducing random effects can not be handled by classical methods. Bayesian approaches using predictive distributions can, though the formal solution, which includes Bayes factors as a specia ..."
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Cited by 59 (10 self)
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Model choice is a fundamental and much discussed activity in the analysis of data sets. Hierarchical models introducing random effects can not be handled by classical methods. Bayesian approaches using predictive distributions can, though the formal solution, which includes Bayes factors as a special case, can be criticized. We propose a predictive criterion where the goal is good prediction of a replicate of the observed data but tempered by fidelity to the observed values. We obtain this criterion by minimizing posterior loss for a given model and then, for models under consideration, select the one which minimizes this criterion. For a broad range of losses, the criterion emerges approximately as a form partitioned into a goodnessoffit term and a penalty term. In the context of generalized linear mixed effects models we obtain a penalized deviance criterion comprised of a piece which is a Bayesian deviance measure and a piece which is a penalty for model complexity. We illustrate ...
Bayesian Variable and Link Determination for Generalised Linear Models
, 2000
"... this paper, we describe full Bayesian inference for generalised linear models where uncertainty ..."
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Cited by 10 (2 self)
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this paper, we describe full Bayesian inference for generalised linear models where uncertainty
Bayesian covariance selection in generalized linear mixed models
 Biometrics
, 2006
"... SUMMARY. The generalized linear mixed model (GLMM), which extends the generalized linear model (GLM) to incorporate random effects characterizing heterogeneity among subjects, is widely used in analyzing correlated and longitudinal data. Although there is often interest in identifying the subset of ..."
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Cited by 8 (3 self)
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SUMMARY. The generalized linear mixed model (GLMM), which extends the generalized linear model (GLM) to incorporate random effects characterizing heterogeneity among subjects, is widely used in analyzing correlated and longitudinal data. Although there is often interest in identifying the subset of predictors that have random effects, random effects selection can be challenging, particularly when outcome distributions are nonnormal. This article proposes a fully Bayesian approach to the problem of simultaneous selection of fixed and random effects in GLMMs. Integrating out the random effects induces a covariance structure on the multivariate outcome data, and an important problem which we also consider is that of covariance selection. Our approach relies on variable selectiontype mixture priors for the components in a special LDU decomposition of the random effects covariance. A stochastic search MCMC algorithm is developed, which relies on Gibbs sampling, with Taylor series expansions used to approximate intractable integrals. Simulated data examples are presented for different exponential family distributions, and the approach is applied to discrete survival data from a timetopregnancy study.
A SimulationIntensive Approach for Checking Hierarchical Models
 TEST
, 1998
"... Recent computational advances have made it feasible to fit hierarchical models in a wide range of serious applications. If one entertains a collection of such models for a given data set, the problems of model adequacy and model choice arise. We focus on the former. While model checking usually addr ..."
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Cited by 8 (0 self)
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Recent computational advances have made it feasible to fit hierarchical models in a wide range of serious applications. If one entertains a collection of such models for a given data set, the problems of model adequacy and model choice arise. We focus on the former. While model checking usually addresses the entire model specification, model failures can occur at each hierarchical stage. Such failures include outliers, mean structure errors, dispersion misspecification, and inappropriate exchangeabilities. We propose another approach which is entirely simulation based. It only requires the model specification and that, for a given data set, one be able to simulate draws from the posterior under the model. By replicating a posterior of interest using data obtained under the model we can "see" the extent of variability in such a posterior. Then, we can compare the posterior obtained under the observed data with this medley of posterior replicates to ascertain whether the former is in agr...
Identifying outliers in Bayesian hierarchical models: a simulationbased approach
"... Abstract. A variety of simulationbased techniques have been proposed for detection of divergent behaviour at each level of a hierarchical model. We investigate a diagnostic test based on measuring the conflict between two independent sources of evidence regarding a parameter: that arising from its ..."
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Cited by 5 (0 self)
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Abstract. A variety of simulationbased techniques have been proposed for detection of divergent behaviour at each level of a hierarchical model. We investigate a diagnostic test based on measuring the conflict between two independent sources of evidence regarding a parameter: that arising from its predictive prior given the remainder of the data, and that arising from its likelihood. This test gives rise to a pvalue that exactly matches or closely approximates a crossvalidatory predictive comparison, and yet is more widely applicable. Its properties are explored for normal hierarchical models and in an application in which divergent surgical mortality was suspected. Since full crossvalidation is so computationally demanding, we examine fulldata approximations which are shown to have only moderate conservatism in normal models. A second example concerns criticism of a complex growth curve model at both observation and parameter levels, and illustrates the issue of dealing with multiple pvalues within a Bayesian framework. We conclude with the proposal of an overall strategy to detecting divergent behaviour in hierarchical models.
Variable Selection in Nonparametric Random Effects Models
"... In analyzing longitudinal or clustered data with a mixed effects model (Laird and Ware, 1982), one may be concerned about violations of normality. Such violations can potentially impact subset selection for the fixed and random effects components of the model, inferences on the heterogeneity structu ..."
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Cited by 2 (2 self)
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In analyzing longitudinal or clustered data with a mixed effects model (Laird and Ware, 1982), one may be concerned about violations of normality. Such violations can potentially impact subset selection for the fixed and random effects components of the model, inferences on the heterogeneity structure, and the accuracy of predictions. This article focuses on Bayesian methods for subset selection in nonparametric random effects models in which one is uncertain about the predictors to be included and the distribution of their random effects. We characterize the unknown distribution of the individualspecific regression coefficients using a weighted sum of Dirichlet process (DP)distributed latent variables. By using carefullychosen mixture priors for coefficients in the base distributions of the component DPs, we allow fixed and random effects to be effectively dropped out of the model. A stochastic search Gibbs sampler is developed for posterior computation, and the methods are illustrated using simulated data and real data from a multilaboratory bioassay study.
Simulation From NonStandard Distributions Using Envelope Methods
, 2000
"... This paper considers the development of envelope methods as a tool for simulation. Envelope methods are based on the construction of simple envelopes to functions. The proposed envelopes are general, require little input from the user and are based on the concavity structure of the function or some ..."
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Cited by 1 (0 self)
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This paper considers the development of envelope methods as a tool for simulation. Envelope methods are based on the construction of simple envelopes to functions. The proposed envelopes are general, require little input from the user and are based on the concavity structure of the function or some transformation of the function. The construction of these envelopes facilitates variate generation using the adaptive rejection algorithm.
Nonparametric GoodnessofFit
"... This paper develops an approach to testing the adequacy of both classical and Bayesian models given univariate sample data. An important feature of the approach is that we are able to test the practical scientific hypothesis of whether the true underlying model is close to some hypothesized model. T ..."
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Cited by 1 (1 self)
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This paper develops an approach to testing the adequacy of both classical and Bayesian models given univariate sample data. An important feature of the approach is that we are able to test the practical scientific hypothesis of whether the true underlying model is close to some hypothesized model. The notion of closeness is based on measurement precision and requires the introduction of a metric for which we consider the Kolmogorov distance. The approach is nonparametric in the sense that the alternative model is a Dirichlet process. Keywords : Monte Carlo, hypothesis testing, nonparametric Bayesian inference, prior elicitation. 1. INTRODUCTION Although Bayesian applications have seen unprecedented growth in the last 10 years, there is no consensus on the correct approach to Bayesian model checking. A selection of diverse approaches that address Bayesian model checking includes Guttman (1967), Guttman, Dutter and Freeman (1978), Chaloner and Brant (1988), Weiss (1994), Gelman, Meng ...
: www.idealibrary.com on An Introduction to Model Selection
"... This paper is an introduction to model selection intended for nonspecialists who have knowledge of the statistical concepts covered in a typical first ..."
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This paper is an introduction to model selection intended for nonspecialists who have knowledge of the statistical concepts covered in a typical first
Mail Stop 10R
"... ETS research prior to publication. They are available without charge from: Research Publications Office ..."
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ETS research prior to publication. They are available without charge from: Research Publications Office