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21
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.
Binary models for marginal independence
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B
, 2005
"... A number of authors have considered multivariate Gaussian models for marginal independence. In this paper we develop models for binary data with the same independence structure. The models can be parameterized based on Möbius inversion and maximum likelihood estimation can be performed using a versi ..."
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Cited by 16 (2 self)
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A number of authors have considered multivariate Gaussian models for marginal independence. In this paper we develop models for binary data with the same independence structure. The models can be parameterized based on Möbius inversion and maximum likelihood estimation can be performed using a version of the Iterated Conditional Fitting algorithm. The approach is illustrated on a simple example. Relations to multivariate logistic and dependence ratio models are discussed.
Composite Multiclass Losses
"... We consider loss functions for multiclass prediction problems. We show when a multiclass loss can be expressed as a “proper composite loss”, which is the composition of a proper loss and a link function. We extend existing results for binary losses to multiclass losses. We determine the stationarity ..."
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Cited by 9 (5 self)
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We consider loss functions for multiclass prediction problems. We show when a multiclass loss can be expressed as a “proper composite loss”, which is the composition of a proper loss and a link function. We extend existing results for binary losses to multiclass losses. We determine the stationarity condition, Bregman representation, ordersensitivity, existence and uniqueness of the composite representation for multiclass losses. We subsume existing results on “classification calibration ” by relating it to properness and show that the simple integral representation for binary proper losses can not be extended to multiclass losses. 1
Bayesian Multivariate Logistic Regression
 Biometrics
, 2004
"... This article proposes a new multivariate logistic density, derived by transforming variables that follow a multivariate t distribution. The resulting logistic density is closely approximated by a multivariate t distribution, has an unrestricted correlation structure, and has properties that facilita ..."
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Cited by 8 (2 self)
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This article proposes a new multivariate logistic density, derived by transforming variables that follow a multivariate t distribution. The resulting logistic density is closely approximated by a multivariate t distribution, has an unrestricted correlation structure, and has properties that facilitate efficient computation
PARAMETERIZATIONS AND FITTING OF BIDIRECTED GRAPH MODELS TO CATEGORICAL DATA
, 2008
"... Abstract. We discuss two parameterizations of models for marginal independencies for discrete distributions which are representable by bidirected graph models, under the global Markov property. Such models are useful data analytic tools especially if used in combination with other graphical models. ..."
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Cited by 4 (1 self)
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Abstract. We discuss two parameterizations of models for marginal independencies for discrete distributions which are representable by bidirected graph models, under the global Markov property. Such models are useful data analytic tools especially if used in combination with other graphical models. The first parameterization, in the saturated case, is also known as the multivariate logistic transformation, the second is a variant that allows, in some (but not all) cases, variation independent parameters. An algorithm for maximum likelihood fitting is proposed, based on an extension of the Aitchison and Silvey method.
Sequences of regressions and their independences
, 2012
"... Ordered sequences of univariate or multivariate regressions provide statistical modelsfor analysingdata fromrandomized, possiblysequential interventions, from cohort or multiwave panel studies, but also from crosssectional or retrospective studies. Conditional independences are captured by what we ..."
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Cited by 4 (1 self)
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Ordered sequences of univariate or multivariate regressions provide statistical modelsfor analysingdata fromrandomized, possiblysequential interventions, from cohort or multiwave panel studies, but also from crosssectional or retrospective studies. Conditional independences are captured by what we name regression graphs, provided the generated distribution shares some properties with a joint Gaussian distribution. Regression graphs extend purely directed, acyclic graphs by two types of undirected graph, one type for components of joint responses and the other for components of the context vector variable. We review the special features and the history of regression graphs, prove criteria for Markov equivalence anddiscussthenotion of simpler statistical covering models. Knowledgeof Markov equivalence provides alternative interpretations of a given sequence of regressions, is essential for machine learning strategies and permits to use the simple graphical criteria of regression graphs on graphs for which the corresponding criteria are in general more complex. Under the known conditions that a Markov equivalent directed acyclic graph exists for any given regression graph, we give a polynomial time algorithm to find one such graph.
A Note on Multivariate Logistic Models for Contingency Tables
 Austral. J. Statist
, 1997
"... Loglinear models are a widely accepted tool for modeling discrete data given in a contingency table. Although their parameters reflect the interaction structure in the joint distribution of all variables, they do not give information about structures appearing in the margins of the table. This is i ..."
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Cited by 3 (0 self)
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Loglinear models are a widely accepted tool for modeling discrete data given in a contingency table. Although their parameters reflect the interaction structure in the joint distribution of all variables, they do not give information about structures appearing in the margins of the table. This is in contrast to multivariate logistic parameters recently introduced by Glonek & McCullagh (1995). They have as parameters the highest order log odds ratios derived from the joint table and from each marginal table. The link between the cell probabilities and the multivariate logistic parameters is given in Glonek & McCullagh in an algebraic fashion. In this paper we focus on this link, showing that it is derived by general parameter transformations in exponential families. In particular, the connection between the natural, the expectation and the mixed parameterization in exponential families (BarndorffNielsen, 1978) is used. This also yields the derivatives of the likelihood equation and shows properties of the Fisher matrix. Further emphasis is paid to the analysis of independence hypotheses in margins of a contingency table.
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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Cited by 2 (1 self)
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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...
Analyzing Incomplete Discrete Longitudinal Clinical Trial Data
, 2006
"... Abstract. Commonly used methods to analyze incomplete longitudinal clinical trial data include complete case analysis (CC) and last observation carried forward (LOCF). However, such methods rest on strong assumptions, including missing completely at random (MCAR) for CC and unchanging profile after ..."
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Cited by 1 (1 self)
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Abstract. Commonly used methods to analyze incomplete longitudinal clinical trial data include complete case analysis (CC) and last observation carried forward (LOCF). However, such methods rest on strong assumptions, including missing completely at random (MCAR) for CC and unchanging profile after dropout for LOCF. Such assumptions are too strong to generally hold. Over the last decades, a number of full longitudinal data analysis methods have become available, such as the linear mixed model for Gaussian outcomes, that are valid under the much weaker missing at random (MAR) assumption. Such a method is useful, even if the scientific question is in terms of a single time point, for example, the last planned measurement occasion, and it is generally consistent with the intentiontotreat principle. The validity of such a method rests on the use of maximum likelihood, under which the missing data mechanism is ignorable as soon as it is MAR. In this paper, we will focus on nonGaussian outcomes, such as