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Hierarchical multilinear models for multiway data

  • Hoff, Peter D.
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    Reduced-rank decompositions provide descriptions of the variation among the elements of a matrix or array. In such decompositions, the elements of an array are expressed as products of low-dimensional latent factors. This article presents a model-based version of such a decomposition, extending the scope of reduced-rank methods to accommodate a variety of data types such as longitudinal social networks and continuous multivariate data that are cross-classified by categorical variables. The proposed model-based approach is hierarchical, in that the latent factors corresponding to a given dimension of the array are not a priori independent, but exchangeable. Such a hierarchical approach allows more flexibility in the types of patterns that can be represented.

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    File URL: http://www.sciencedirect.com/science/article/B6V8V-505F9BR-2/2/ff420b2d79a4726a3802ef876bb752bd
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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 55 (2011)
    Issue (Month): 1 (January)
    Pages: 530-543

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    Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:530-543
    Contact details of provider: Web page: http://www.elsevier.com/locate/csda

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    1. Joseph Kruskal, 1976. "More factors than subjects, tests and treatments: An indeterminacy theorem for canonical decomposition and individual differences scaling," Psychometrika, Springer, vol. 41(3), pages 281-293, September.
    2. Tsukuma, Hisayuki, 2009. "Generalized Bayes minimax estimation of the normal mean matrix with unknown covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2296-2304, November.
    3. Tsukuma, Hisayuki, 2008. "Admissibility and minimaxity of Bayes estimators for a normal mean matrix," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2251-2264, November.
    4. Boik, Robert J., 1989. "Reduced-rank models for interaction in unequally replicated two-way classifications," Journal of Multivariate Analysis, Elsevier, vol. 28(1), pages 69-87, January.
    5. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika van der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639.
    6. Tomasi, Giorgio & Bro, Rasmus, 2006. "A comparison of algorithms for fitting the PARAFAC model," Computational Statistics & Data Analysis, Elsevier, vol. 50(7), pages 1700-1734, April.
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