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44
Data augmentation in multiway contingency tables with fixed marginal totals
 JOURNAL OF STATISTICAL PLANNING AND INFERENCE
, 2006
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Univariate and Bivariate Loglinear Models for Discrete Test Score Distributions
, 2000
"... The welldeveloped theory of exponential families of distributions is applied to the problem of fitting the univariate histograms and discrete bivariate frequency distributions that often arise in the analysis of test scores. These models are powerful tools for many forms of parametric data smoothi ..."
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The welldeveloped theory of exponential families of distributions is applied to the problem of fitting the univariate histograms and discrete bivariate frequency distributions that often arise in the analysis of test scores. These models are powerful tools for many forms of parametric data smoothing and are particularly wellsuited to problems in which there is little or no theory to guide a choice of probability models, e.g., smoothing a distribution to eliminate roughness and zero frequencies in order to equate scores from different tests. Attention is given to efficient computation of the maximum likelihood estimates of the parameters using Newton's Method and to computationally efficient methods for obtaining the asymptotic standard errors of the fitted frequencies and proportions. We discuss tools that can be used to diagnose the quality of the fitted frequencies for both the univariate and the bivariate cases. Five examples, using real data, are used to illustrate the methods of this paper.
An Iterative Method for Solving Linear Inequalities
, 1987
"... This paper describes and analyzes a method for finding nontrivial solutions of the inequality Ax 0, where A is an m \Theta n matrix of rank n. The method is based on the observation that a certain function f has a unique minimum if and only if the inequality ..."
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This paper describes and analyzes a method for finding nontrivial solutions of the inequality Ax 0, where A is an m \Theta n matrix of rank n. The method is based on the observation that a certain function f has a unique minimum if and only if the inequality
Characterizations of Decomposable Dependency Models
 Journal of Artificial Intelligence Research
, 1996
"... Decomposable dependency models possess a number of interesting and useful properties. This paper presents new characterizations of decomposable models in terms of independence relationships, which are obtained by adding a single axiom to the wellknown set characterizing dependency models that are i ..."
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Decomposable dependency models possess a number of interesting and useful properties. This paper presents new characterizations of decomposable models in terms of independence relationships, which are obtained by adding a single axiom to the wellknown set characterizing dependency models that are isomorphic to undirected graphs. We also briefly discuss a potential application of our results to the problem of learning graphical models from data. 1. Introduction Graphical models are knowledge representation tools commonly used by an increasing number of researchers, particularly from the Artificial Intelligence and Statistics communities. The reason for the success of graphical models is their capacity to represent and handle independence relationships, which have proved crucial for the efficient management and storage of information (Pearl, 1988). There are different kinds of graphical models, although we are particularly interested in undirected and directed graphs (which, in a proba...
Testing the Rasch Model via Sequential Importance Sampling
, 2003
"... Rasch proposed an exact conditional inference approach to testing his model but never implemented it because it involves the calculation of a complicated probability. This paper furthers Rasch's approach by (1) providing an efficient Monte Carlo methodology for accurately approximating the required ..."
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Rasch proposed an exact conditional inference approach to testing his model but never implemented it because it involves the calculation of a complicated probability. This paper furthers Rasch's approach by (1) providing an efficient Monte Carlo methodology for accurately approximating the required probability and (2) illustrating the usefulness of Rasch's approach for several problems by developing appropriate test statistics and examining their properties through simulation studies. Our Monte Carlo methodology is shown to compare favorably to other Monte Carlo methods proposed for this problem in two respects: it is considerably faster and it provides more reliable estimates of the Monte Carlo standard error.
Bayesian Inference in Incomplete MultiWay Tables
 Journal of Statistical Planning and Inference
, 2003
"... We describe and illustrate approaches to Bayesian inference in multiway contigency tables for which partial information... ..."
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We describe and illustrate approaches to Bayesian inference in multiway contigency tables for which partial information...
Algebraic Descriptions of Nominal Multivariate Discrete Data
 J. Multivariate Anal
, 1995
"... Traditionally, multivariate discrete data are analyzed by means of loglinear models. In this paper we show how an algebraic approach leads naturally to alternative models, parametrized in terms of the moments of the distribution. Moreover we derive a complete characterization of all meaningful tran ..."
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Traditionally, multivariate discrete data are analyzed by means of loglinear models. In this paper we show how an algebraic approach leads naturally to alternative models, parametrized in terms of the moments of the distribution. Moreover we derive a complete characterization of all meaningful transformations of the components and show how transformations affect the moments of a distribution. It turns out that our models provide the necessary formal description of longitudinal data; moreover in the classical case, they can be considered as an analysis tool, complementary to loglinear models. 1 Introduction We start with a given multivariate discrete nominal variable X. Questions of interest about X can be roughly divided into two groups. One group is related to conditional characteristics such as conditional independencies or questions concerning the sign and/or magnitude of logodds ratios. The other group focuses on marginal characteristics such as marginal independencies or multiv...
Context Specific Interaction Models
, 1999
"... Interaction models for categorical data play a central role in applied statistics. In particular, decomposable models have obtained a dominant position as the basis for structural learning and the development of efficient computational algorithms in connection with Bayesian networks for decision sup ..."
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Interaction models for categorical data play a central role in applied statistics. In particular, decomposable models have obtained a dominant position as the basis for structural learning and the development of efficient computational algorithms in connection with Bayesian networks for decision support. The present paper generalizes decomposable models to cover log linear models, where interactions may be present only in specific contexts (CSImodels). It is shown that the model function of a decomposable CSImodel has a factorization in terms of marginals. It is illustrated that this provides a much richer class of operational models, which must be expected to be the starting point for the development of a new generation of effective computational algorithms for decision support systems based on Bayesian networks with context specific independencies. Key words: context specific interaction, context specific independence, decomposable model, factorization, probability tree, exact Baysian inference. 1
The Admissibility Of The Maximum Likelihood Estimator For Decomposable LogLinear Interaction Models For Contingency Tables
, 1998
"... It is well known that for certain loglinear interaction models for contingency tables, i.e. those that are decomposable, the maximum likelihood estimator can be found explicitly. In this note we will show that in such cases this estimator is admissible. The proof is based on a stepwise Bayes argume ..."
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It is well known that for certain loglinear interaction models for contingency tables, i.e. those that are decomposable, the maximum likelihood estimator can be found explicitly. In this note we will show that in such cases this estimator is admissible. The proof is based on a stepwise Bayes argument and is a generalization of a proof of the admissibility of the maximum likelihood estimator for the usual unconstrained multinomial model. It is then shown that this result is a special case of a result for discrete exponential families. 1. INTRODUCTION In loglinear models for contingency tables maximum likelihood is the standard method of estimation. For certain hierarchical models, called decomposable models, (see Goodman (1970, 1971) and Andersen (1974)) it was shown in Haberman (1974) that the maximum likelihood estimator could be found explicitly. Darroch, Lauritzen and Speed (1980) considered a certain class of graphical models which contains the family of hierarchical models. T...
Graphical model, messagepassing algorithms and convex optimization. [Online]. Available: http://www.eecs.berkeley. edu/ âˆ¼wainwrig/Talks/A GraphModel Tutorial.pdf
, 2003
"... Graphical models provide a framework for describing statistical dependencies in (possibly large) collections of random variables. At their core lie various correspondences between the conditional independence properties of a random vector, and the structure of an underlying graph used to represent i ..."
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Graphical models provide a framework for describing statistical dependencies in (possibly large) collections of random variables. At their core lie various correspondences between the conditional independence properties of a random vector, and the structure of an underlying graph used to represent its distribution. They