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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 435 (4 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 180 (13 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 51 (8 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 42 (4 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 31 (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
Efficiency of the generalized estimating equations for binary response
 Journal of the Royal Statistical Society Series B
"... Summary. Using standard correlation bounds, we show that in generalized estimation equations (GEEs) the socalled ‘working correlation matrix ’ R.α / for analysing binary data cannot in general be the true correlation matrix of the data.Methods for estimating the correlation parameter in current G ..."
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Cited by 14 (0 self)
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Summary. Using standard correlation bounds, we show that in generalized estimation equations (GEEs) the socalled ‘working correlation matrix ’ R.α / for analysing binary data cannot in general be the true correlation matrix of the data.Methods for estimating the correlation parameter in current GEE software for binary responses disregard these bounds. To show that the GEE applied on binary data has high efficiency, we use a multivariate binary model so that the covariance matrix from estimating equation theory can be compared with the inverse Fisher information matrix. But R.α / should be viewed as the weight matrix, and it should not be confused with the correlation matrix of the binary responses. We also do a comparison with more general weighted estimating equations by using a matrix Cauchy–Schwarz inequality. Our analysis leads to simple rules for the choice of α in an exchangeable or autoregressive AR(1) weight matrix R.α/, based on the strength of dependence between the binary variables. An example is given to illustrate the assessment of dependence and choice of α.
Extended generalized estimating equations for clustered data
 Journal of the American Statistical Association
, 1998
"... ..."
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 8 (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).
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).
2000. “In and Out of War and Peace: transitional models of international conflict.” Working Paper
"... Dyadyear data on international conflict are simultaneously qualitative and serially dependent. Extending Beck, Katz, and Tucker’s (1998) methodological contribution, I propose transitional models that deal with these two features of the data. These statistical models explicitly deal with the way a ..."
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Cited by 6 (0 self)
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Dyadyear data on international conflict are simultaneously qualitative and serially dependent. Extending Beck, Katz, and Tucker’s (1998) methodological contribution, I propose transitional models that deal with these two features of the data. These statistical models explicitly deal with the way a dyad’s particular history of peace or conflict structures current outcomes, consistent with important substantive notions in the IR literature such as reputationbuilding, signalling, alliance reliability, territoriality, and enduring rivalries. That is, I propose statistical models that (a) are easily estimated; (b) resolve longstanding methodological dilemmas, and (c) speak to important theoretical ideas in the study of international relations. The transitional models I propose generalize beyond the international conflict data analyzed here, to any type of discrete timeseries setting. One of the transitional models I propose is a novel methodological contribution in its own right a dynamic probit model unifying two hitherto disparate branches of quantitative political methodology (time series and discrete choice). 1 Dyadyear data on international conflict are widely used in quantitative studies of international relations.