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Hierarchical multilinear models for multiway data

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  • Hoff, Peter D.

Abstract

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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    2. 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.
    3. Silvia D'Angelo & Marco Alfò & Thomas Brendan Murphy, 2020. "Modeling node heterogeneity in latent space models for multidimensional networks," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(3), pages 324-341, August.
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    5. Hill, L.M. & Moody, J. & Gottfredson, N.C. & Kajula, L.J. & Pence, B.W. & Go, V.F. & Maman, S., 2018. "Peer norms moderate the association between mental health and sexual risk behaviors among young men living in Dar es Salaam, Tanzania," Social Science & Medicine, Elsevier, vol. 196(C), pages 77-85.
    6. Zhen-Yu Chen & Zhi-Ping Fan & Minghe Sun, 2014. "Ensemble Learning for Cross-Selling Using Multitype Multiway Data," Working Papers 0155mss, College of Business, University of Texas at San Antonio.
    7. 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.
    8. Iddi, Samuel & Molenberghs, Geert, 2012. "A combined overdispersed and marginalized multilevel model," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1944-1951.
    9. Bartolucci, Francesco & Marino, Maria Francesca & Pandolfi, Silvia, 2018. "Dealing with reciprocity in dynamic stochastic block models," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 86-100.

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