Results 1  10
of
16
Bilinear Mixed Effects Models for Dyadic Data
, 2003
"... This article discusses the use of a symmetric multiplicative interaction effect to capture certain types of thirdorder dependence patterns often present in social networks and other dyadic datasets. Such an effect, along with standard linear fixed and random effects, is incorporated into a general ..."
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Cited by 13 (3 self)
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This article discusses the use of a symmetric multiplicative interaction effect to capture certain types of thirdorder dependence patterns often present in social networks and other dyadic datasets. Such an effect, along with standard linear fixed and random effects, is incorporated into a generalized linear model, and a Markov chain Monte Carlo algorithm is provided for Bayesian estimation and inference. In an example analysis of international relations data, accounting for such patterns improves model fit and predictive performance.
Model averaging and dimension selection for the singular value decomposition
 Journal of the American Statistical Association
, 2007
"... Many multivariate data analysis techniques for an m × n matrix Y are related to the model Y = M+E, where Y is an m×n matrix of full rank and M is an unobserved mean matrix of rank K < (m ∧ n). Typically the rank of M is estimated in a heuristic way and then the leastsquares estimate of M is obtaine ..."
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Cited by 7 (1 self)
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Many multivariate data analysis techniques for an m × n matrix Y are related to the model Y = M+E, where Y is an m×n matrix of full rank and M is an unobserved mean matrix of rank K < (m ∧ n). Typically the rank of M is estimated in a heuristic way and then the leastsquares estimate of M is obtained via the singular value decomposition of Y, yielding an estimate that can have a very high variance. In this paper we suggest a modelbased alternative to the above approach by providing prior distributions and posterior estimation for the rank of M and the components of its singular value decomposition. In addition to providing more accurate inference, such an approach has the advantage of being extendable to more general dataanalysis situations, such as inference in the presence of missing data and estimation in a generalized linear modeling framework.
Robust factorization of a data matrix
 In COMPSTAT, Proceedings in Computational Statistics
, 1998
"... Abstract. In this note we show how the entries of a data matrix can be approximated by a sum of row effects, column effects and interaction terms in a robust way using a weighted L1 estimator. We discuss an algorithm to compute this fit, and show by a simulation experiment and an example that the pr ..."
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Cited by 6 (0 self)
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Abstract. In this note we show how the entries of a data matrix can be approximated by a sum of row effects, column effects and interaction terms in a robust way using a weighted L1 estimator. We discuss an algorithm to compute this fit, and show by a simulation experiment and an example that the proposed method can be a useful tool in exploring data matrices. Moreover, a robust biplot is produced as a byproduct.
Analysis of Longitudinal Metabolomics Data
"... Motivation: Metabolomics datasets are generally large and complex. Using Principal Component Analysis (PCA), a simplified view of the variation in the data is obtained. The PCAmodel can be interpreted and the processes underlying the variation in the data can be analysed. In metabolomics often a pr ..."
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Cited by 3 (1 self)
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Motivation: Metabolomics datasets are generally large and complex. Using Principal Component Analysis (PCA), a simplified view of the variation in the data is obtained. The PCAmodel can be interpreted and the processes underlying the variation in the data can be analysed. In metabolomics often a priori information is present about the data. Various forms of this information can be used in an unsupervised data analysis with Weighted PCA (WPCA). A WPCAmodel will give a view on the data that is different from the view obtained using PCA and it will add to the interpretation of the information in a metabolomics dataset. Results: A method is presented to translate spectra of repeated measurements into weights describing the experimental error. These weights are used in a data analysis with WPCA. The WPCAmodel will give a view on the data where the nonuniform experimental error is accounted for. Therefore the WPCA model will focus more on the natural variation in the data. Availability: Mfiles for MATLAB for the algorithm used in this research are
Monitoring and Modeling
 the Cure Processing Properties of Resin Transfer Molding Resins, International SAMPE Symposium and Exhibition
, 1989
"... averaging and dimension selection for the singular value decomposition ..."
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Cited by 1 (0 self)
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averaging and dimension selection for the singular value decomposition
Modeling Dependencies in International Relations Networks
, 2003
"... Despite the desire to focus on the interconnected nature of politics and economics at the global scale, most empirical studies in the field of international relations assume that the major actors are not only sovereign, but also that their relationships are independent phenomena. In contrast, this a ..."
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Despite the desire to focus on the interconnected nature of politics and economics at the global scale, most empirical studies in the field of international relations assume that the major actors are not only sovereign, but also that their relationships are independent phenomena. In contrast, this article illustrates the use of linear and bilinear random effects models to represent statistical dependencies that often characterize dyadic data such as international relations. In particular, we show how to estimate models for dyadic data that simultaneously take into account: a) regressor variables, b) correlation of actions having the same actor, c) correlation of actions having the same target, d) correlation of actions between a pair of actors(i.e. reciprocity of actions), and e) thirdorder dependencies, such as transitivity, clustering, and balance....
DEPÓSITO LEGAL: S.16122004 PUBLISHED BY Departamento de Estadística
, 2004
"... The texts of the various papers in this volume were set individually by the authors or under their supervisión. Only minor corrections to the text have been carried out by the editors. No Responsability is assumed by the Publisher, the Editors and the Authors for any injury and/or damage to persons ..."
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The texts of the various papers in this volume were set individually by the authors or under their supervisión. Only minor corrections to the text have been carried out by the editors. No Responsability is assumed by the Publisher, the Editors and the Authors for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use of operation of any methods, products, instructions or ideas contained in the material herein. © Statistics Department All rights reserved. No part of this publication may be reproduced, stored in retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior writen permission of the Editors.
Lower Rank Approximation of Matrices by Least Squares With Any Choice of Weights
"... Reduced rank approximation of matrices has hitherto been possible only by unweighted least squares. This paper presents iterative techniques for obtaining such approximations when weights are introduced. The techniques involve crisscross regressions with careful initialization. Possible application ..."
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Reduced rank approximation of matrices has hitherto been possible only by unweighted least squares. This paper presents iterative techniques for obtaining such approximations when weights are introduced. The techniques involve crisscross regressions with careful initialization. Possible applications of the approximation are in modelling, biplotting, contingency table analysis, fitting of missing values, checking outliers, etc. KEY WORDS Reduced rank approximation Least squares Crisscross regression HouseholderYoung theorem
AND SOME EXAMPLES OF ITS USE
"... Biplot is an explorative method of data analysis permitting to represent graphically, usually in a plane, the interrelations among pointsvariables and pointsindividuals located in a multivariate space. This is done by making projections from the multivariate space onto two or threedimensional su ..."
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Biplot is an explorative method of data analysis permitting to represent graphically, usually in a plane, the interrelations among pointsvariables and pointsindividuals located in a multivariate space. This is done by making projections from the multivariate space onto two or threedimensional subspaces. The crucial issue is: to what extend the projections in the lower dimension subspaces reflect the true relations of pointsvariables and pointsindividuals in the full data space? It happens that sometimes the representation given by the biplot is a good one, however sometimes it is a bad one and certainly not sufficient. We show exactly wherefrom (i.e. from which theorems) some inferential properties of a biplot can be deduced and under which circumstances the relations visualized in the biplot are trustworthy. We propose to construct the biplot in an extended mode which permits to judge the adequacy of the twodimensional approximation visualized by the classical biplot. We call the biplot drawn in the extended mode the augmented biplot. Several real data examples illustrate the use of the augmented biplot and the broadness and diversity of problems which can be elucidated relatively simply by use of the elaborated technique. Key words and phrases: Data matrix, exploratory data analysis, reduction of dimensionality, graphical representation of multivariate points and interrelations from multivariate space.