Abstract not found

This article discusses the use of a symmetric multiplicative interaction effect to capture certain types of third-order 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.

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.

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 least-squares 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 model-based 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 data-analysis situations, such as inference in the presence of missing data and estimation in a generalized linear modeling framework.

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 not only that the major actors are sovereign, but also that their relationships are portrayed in data that are modeled as 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) third-order dependencies, such as transitivity, clustering, and balance. We apply this new approach to the political relations among a wide range of political actors in Central Asia over the period 1989–1999, illustrating the presence and strength of second- and third-order statistical dependencies in these data. 1

averaging and dimension selection for the singular value decomposition

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 PCA-model 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 WPCA-model 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 WPCA-model will give a view on the data where the non-uniform experimental error is accounted for. Therefore the WPCA model will focus more on the natural variation in the data. Availability: M-files for MATLAB for the algorithm used in this research are

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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 criss-cross 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 Criss-cross regression Householder-Young theorem

Biplot is an explorative method of data analysis permitting to represent graphically, usually in a plane, the interrelations among points-variables and points-individuals located in a multivariate space. This is done by making projections from the multivariate space onto two- or three-dimensional subspaces. The crucial issue is: to what extend the projections in the lower dimension subspaces reflect the true relations of points-variables and points-individuals 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 two-dimensional 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.