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Bayesian measures of model complexity and fit
 Journal of the Royal Statistical Society, Series B
, 2002
"... [Read before The Royal Statistical Society at a meeting organized by the Research ..."
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Cited by 132 (2 self)
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[Read before The Royal Statistical Society at a meeting organized by the Research
Analysis of multivariate probit models
 BIOMETRIKA
, 1998
"... This paper provides a practical simulationbased Bayesian and nonBayesian analysis of correlated binary data using the multivariate probit model. The posterior distribution is simulated by Markov chain Monte Carlo methods and maximum likelihood estimates are obtained by a Monte Carlo version of the ..."
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Cited by 100 (6 self)
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This paper provides a practical simulationbased Bayesian and nonBayesian analysis of correlated binary data using the multivariate probit model. The posterior distribution is simulated by Markov chain Monte Carlo methods and maximum likelihood estimates are obtained by a Monte Carlo version of the EM algorithm. A practical approach for the computation of Bayes factors from the simulation output is also developed. The methods are applied to a dataset with a bivariate binary response, to a fouryear longitudinal dataset from the Six Cities study of the health effects of air pollution and to a sevenvariate binary response dataset on the labour supply of married women from the Panel Survey of Income Dynamics.
Bayesian Deviance, the Effective Number of Parameters, and the Comparison of Arbitrarily Complex Models
, 1998
"... We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. We follow Dempster in examining the posterior distribution of the loglikelihood under each model, from which we derive measures of fit and complexity (the effective number of p ..."
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Cited by 28 (7 self)
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We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. We follow Dempster in examining the posterior distribution of the loglikelihood under each model, from which we derive measures of fit and complexity (the effective number of parameters). These may be combined into a Deviance Information Criterion (DIC), which is shown to have an approximate decisiontheoretic justification. Analytic and asymptotic identities reveal the measure of complexity to be a generalisation of a wide range of previous suggestions, with particular reference to the neural network literature. The contributions of individual observations to fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages. The procedure is illustrated in a number of examples, and throughout it is emphasised that the required quantities are trivial to compute in a Markov chain Monte Carlo analysis, and require no analytic work for new...
On MCMC Sampling in Hierarchical Longitudinal Models
 Statistics and Computing
, 1998
"... this paper we construct several (partially and fully blocked) MCMC algorithms for minimizing the autocorrelation in MCMC samples arising from important classes of longitudinal data models. We exploit an identity used by Chib (1995) in the context of Bayes factor computation to show how the parameter ..."
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Cited by 14 (2 self)
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this paper we construct several (partially and fully blocked) MCMC algorithms for minimizing the autocorrelation in MCMC samples arising from important classes of longitudinal data models. We exploit an identity used by Chib (1995) in the context of Bayes factor computation to show how the parameters in a general linear mixed model may be updated in a single block, improving convergence and producing essentially independent draws from the posterior of the parameters of interest. We also investigate the value of blocking in nonGaussian mixed models, as well as in a class of binary response data longitudinal models. We illustrate the approaches in detail with three realdata examples.
Review of Software to Fit Generalized Estimating Equation Regression Models
 The American Statistician
, 1999
"... this article, we briefly review GLM, the GEE methodology, introduce some examples, and compare the GEE implementations of several general purpose statistical packages (SAS, Stata, SUDAAN, and SPlus). We focus on the user interface, accuracy, and completeness of implementations of this methodology. ..."
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Cited by 12 (1 self)
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this article, we briefly review GLM, the GEE methodology, introduce some examples, and compare the GEE implementations of several general purpose statistical packages (SAS, Stata, SUDAAN, and SPlus). We focus on the user interface, accuracy, and completeness of implementations of this methodology. KEY WORDS: Computer software for statistical analysis; Generalized estimating equations; Missing data. 1. INTRODUCTION Generalized linear models (GLMs) (McCullagh and Nelder 1989) are a standard method used to fit regression models for univariate data that are presumed to follow an exponential family distribution. Frequently researchers are interested in analyzing data that arise from a longitudinal, repeated measures or clustered design, and there exists correlation between observations on a given subject. If the outcomes are approximately multivariate normal, then there are well established methods of analysis (Laird and Ware 1982) that have been widely implemented in ge
Marginal regression modeling of correlated multicategorical response: A likelihood approach
 Discussion paper 19, SFB 386, LudwigMaximilians Universitat, Munchen
, 1996
"... A full likelihood approach for marginal regression modeling of correlated multicategorical data is proposed. It is in fact an extension of the approach of Fitzmaurice and Laird (1993) for repeated binary response. The association is directly modeled in terms of conditional odds ratio parameters resu ..."
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Cited by 7 (2 self)
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A full likelihood approach for marginal regression modeling of correlated multicategorical data is proposed. It is in fact an extension of the approach of Fitzmaurice and Laird (1993) for repeated binary response. The association is directly modeled in terms of conditional odds ratio parameters resulting in the fact that the maximum likelihood estimates of mean and association parameters are asymptotically independent. The technical details are worked out and the approach is illustrated with data previously analyzed by Miller, Davis and Landis (1993).
Non and Semiparametric Marginal Regression Models for Ordinal Response
, 1997
"... this paper, we focus attention on cumulative regression models for ordinal responses (McCullagh, 1980) and multivariate extensions. Such models exploit, in a parsimonious way, the ordered scale of the outcomes. An important example for a cumulative model is the wellknown proportional odds model. T ..."
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Cited by 6 (2 self)
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this paper, we focus attention on cumulative regression models for ordinal responses (McCullagh, 1980) and multivariate extensions. Such models exploit, in a parsimonious way, the ordered scale of the outcomes. An important example for a cumulative model is the wellknown proportional odds model. This and other ordinal response models have been discussed in detail by Fahrmeir and Tutz (1994, ch. 3).
Extended Generalized Estimating Equations for Clustered Data
 J. Am. Statist. Ass
, 1997
"... Typically, the analysis of data consisting of multiple observations on a cluster is complicated by withincluster correlation. Estimating equations for generalized linear modelling of clustered data have recently received much attention. This paper proposes an extension to the generalized estimating ..."
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Cited by 3 (3 self)
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Typically, the analysis of data consisting of multiple observations on a cluster is complicated by withincluster correlation. Estimating equations for generalized linear modelling of clustered data have recently received much attention. This paper proposes an extension to the generalized estimating equation method proposed by Liang and Zeger (1986). Liang and Zeger's approach was to treat withincluster correlations as nuisance parameters. This paper, using ideas from extended quasilikelihood, provides estimating equations for regression and association parameters simultaneously. The resulting estimators are proven to be asymptotically normal and consistent under certain conditions. The consistency of regression estimators allows incorrect modelling of the correlation among repeated responses. The method is illustrated with an analysis of data from a developmental toxicity study. KEY WORDS: Correlation, Extended quasilikelihood, Generalized linear models, Longitudinal data, Marginal ...
Multivariate Probit Analysis of Binary Time Series Data with Missing Responses
, 1996
"... The development of adequate models for binary time series data with covariate adjustment has been an active research area in the last years. In the case, where interest is focused on marginal and association parameters, generalized estimating equations (GEE) (see for example Lipsitz, ..."
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Cited by 2 (1 self)
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The development of adequate models for binary time series data with covariate adjustment has been an active research area in the last years. In the case, where interest is focused on marginal and association parameters, generalized estimating equations (GEE) (see for example Lipsitz,
Penalized Multivariate Logistic Regression With A Large Data Set
, 1999
"... We combine a smoothing spline ANOVA model and a loglinear model to build a partly exible model for multivariate Bernoulli data. The joint distribution conditioning on the predictor variables is estimated. The conditional log odds ratio is used to measure the association between outcome variables. A ..."
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We combine a smoothing spline ANOVA model and a loglinear model to build a partly exible model for multivariate Bernoulli data. The joint distribution conditioning on the predictor variables is estimated. The conditional log odds ratio is used to measure the association between outcome variables. A numerical scheme based on the block onestep SORNewtonRalphson algorithm is proposed to obtain an approximate solution for the variational problem. It is proved for a special case that the approximate solution can achieve the same statistical convergence rate as the exact solution, but is much more computing ecient. We extend GACV (Generalized Approximate Cross Validation) to the case of multivariate Bernoulli responses. Its randomized version is fast and stable to compute. Simulation studies show that it is an excellent computational proxy for the CKL (Comparative KullbackLeibler) distance. It is used to adaptively select smoothing parameters in each block onestep SOR iteration. Approximate Bayesian condence intervals are obtained for the exible estimates of the conditional logit functions. Simulation studies are conducted to check the performance of the proposed method. Finally, the model is applied to twoeye observational data from the Beaver Dam Eye Study to examine the association of pigmentary abnormalities and various covariates. ii Acknowledgements I would like to express my deepest gratitude to my advisor, Professor Grace Wahba. She initiated the research described in this dissertation and her dedication to statistics has been a tremendous inspiration to me. During the course of this study we had many fruitful discussions and she provided me numerous insightful suggestions. I shall always appreciate her guidance which led me into the wonderful world of smo...