IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v55y2011i1p530-543.html
   My bibliography  Save this article

Hierarchical multilinear models for multiway data

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(10)00221-5
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Michael D. Ward & Randolph M. Siverson & Xun Cao, 2007. "Disputes, Democracies, and Dependencies: A Reexamination of the Kantian Peace," American Journal of Political Science, John Wiley & Sons, vol. 51(3), pages 583-601, July.
    4. 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, October.
    5. 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.
    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.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. Linardi, Fernando & Diks, Cees & van der Leij, Marco & Lazier, Iuri, 2020. "Dynamic interbank network analysis using latent space models," Journal of Economic Dynamics and Control, Elsevier, vol. 112(C).
    4. 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.
    5. 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.
    6. Iddi, Samuel & Molenberghs, Geert, 2012. "A combined overdispersed and marginalized multilevel model," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1944-1951.
    7. 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.
    8. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tsukuma, Hisayuki, 2010. "Shrinkage priors for Bayesian estimation of the mean matrix in an elliptically contoured distribution," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1483-1492, July.
    2. Zinodiny, S. & Rezaei, S. & Nadarajah, S., 2017. "Bayes minimax estimation of the mean matrix of matrix-variate normal distribution under balanced loss function," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 110-120.
    3. Hu, Guikai & Peng, Ping, 2012. "Matrix linear minimax estimators in a general multivariate linear model under a balanced loss function," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 286-295.
    4. Shokofeh Zinodiny & Saralees Nadarajah, 2024. "A New Class of Bayes Minimax Estimators of the Mean Matrix of a Matrix Variate Normal Distribution," Mathematics, MDPI, vol. 12(7), pages 1-14, April.
    5. Buddhavarapu, Prasad & Bansal, Prateek & Prozzi, Jorge A., 2021. "A new spatial count data model with time-varying parameters," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 566-586.
    6. Mumtaz, Haroon & Theodoridis, Konstantinos, 2017. "Common and country specific economic uncertainty," Journal of International Economics, Elsevier, vol. 105(C), pages 205-216.
    7. Christina Leuker & Thorsten Pachur & Ralph Hertwig & Timothy J. Pleskac, 2019. "Do people exploit risk–reward structures to simplify information processing in risky choice?," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 5(1), pages 76-94, August.
    8. Rubio, F.J. & Steel, M.F.J., 2011. "Inference for grouped data with a truncated skew-Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3218-3231, December.
    9. Alessandri, Piergiorgio & Mumtaz, Haroon, 2019. "Financial regimes and uncertainty shocks," Journal of Monetary Economics, Elsevier, vol. 101(C), pages 31-46.
    10. Svetlana V. Tishkovskaya & Paul G. Blackwell, 2021. "Bayesian estimation of heterogeneous environments from animal movement data," Environmetrics, John Wiley & Sons, Ltd., vol. 32(6), September.
    11. Leonardo Oliveira Martins & Hirohisa Kishino, 2010. "Distribution of distances between topologies and its effect on detection of phylogenetic recombination," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(1), pages 145-159, February.
    12. Tamal Ghosh & Malay Ghosh & Jerry J. Maples & Xueying Tang, 2022. "Multivariate Global-Local Priors for Small Area Estimation," Stats, MDPI, vol. 5(3), pages 1-16, July.
    13. Eibich, Peter & Ziebarth, Nicolas, 2014. "Examining the Structure of Spatial Health Effects in Germany Using Hierarchical Bayes Models," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 49, pages 305-320.
    14. Wu, Ji & Guo, Mengmeng & Chen, Minghua & Jeon, Bang Nam, 2019. "Market power and risk-taking of banks: Some semiparametric evidence from emerging economies," Emerging Markets Review, Elsevier, vol. 41(C).
    15. repec:jss:jstsof:21:i08 is not listed on IDEAS
    16. Deng, Yaguo & Lopes Moreira Da Veiga, María Helena & Wiper, Michael Peter, 2016. "Efficiency evaluation of Spanish hotel chains," DES - Working Papers. Statistics and Econometrics. WS 23897, Universidad Carlos III de Madrid. Departamento de Estadística.
    17. Cathy W. S. Chen & Sangyeol Lee, 2017. "Bayesian causality test for integer-valued time series models with applications to climate and crime data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(4), pages 797-814, August.
    18. Makoto Chikaraishi & Akimasa Fujiwara & Junyi Zhang & Kay Axhausen, 2011. "Identifying variations and co-variations in discrete choice models," Transportation, Springer, vol. 38(6), pages 993-1016, November.
    19. Galatia Cleanthous & Emilio Porcu & Philip White, 2021. "Regularity and approximation of Gaussian random fields evolving temporally over compact two-point homogeneous spaces," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 836-860, December.
    20. Baños-Pino, José F. & Boto-García, David & Zapico, Emma, 2021. "Persistence and dynamics in the efficiency of toll motorways: The Spanish case," Efficiency Series Papers 2021/03, University of Oviedo, Department of Economics, Oviedo Efficiency Group (OEG).
    21. Xing Ju Lee & Christopher C. Drovandi & Anthony N. Pettitt, 2015. "Model choice problems using approximate Bayesian computation with applications to pathogen transmission data sets," Biometrics, The International Biometric Society, vol. 71(1), pages 198-207, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:530-543. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.