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Hierarchical multilinear models for multiway data


  • Hoff, Peter D.


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.

Suggested Citation

  • Hoff, Peter D., 2011. "Hierarchical multilinear models for multiway data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 530-543, January.
  • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:530-543

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    References listed on IDEAS

    1. Joseph Kruskal, 1976. "More factors than subjects, tests and treatments: An indeterminacy theorem for canonical decomposition and individual differences scaling," Psychometrika, Springer;The Psychometric Society, vol. 41(3), pages 281-293, September.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
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    Cited by:

    1. Fan, Zhi-Ping & Sun, Minghe, 2016. "A multi-kernel support tensor machine for classification with multitype multiway data and an application to cross-selling recommendationsAuthor-Name: Chen, Zhen-Yu," European Journal of Operational Research, Elsevier, vol. 255(1), pages 110-120.
    2. Iddi, Samuel & Molenberghs, Geert, 2012. "A combined overdispersed and marginalized multilevel model," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1944-1951.
    3. Fernando Linardi & Cees (C.G.H.) Diks & Marco (M.J.) van der Leij & Iuri Lazier, 2017. "Dynamic Interbank Network Analysis Using Latent Space Models," Tinbergen Institute Discussion Papers 17-101/II, Tinbergen Institute.
    4. Ohlson, Martin & Rauf Ahmad, M. & von Rosen, Dietrich, 2013. "The multilinear normal distribution: Introduction and some basic properties," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 37-47.


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