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On matrix-variate regression analysis

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  • Viroli, Cinzia

Abstract

Three-way data arise in different application domains when multiple responses are measured at different time points or locations. A new regression model for analyzing three-way data is proposed. By assuming the matrix normal distribution for the error term, we will show that the proposed model represents the natural generalization of multiple and multivariate regression analysis. Inferential properties of the model estimators are derived. The model fit is illustrated on a real application.

Suggested Citation

  • Viroli, Cinzia, 2012. "On matrix-variate regression analysis," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 296-309.
    • Handle: RePEc:eee:jmvana:v:111:y:2012:i:c:p:296-309
    DOI: 10.1016/j.jmva.2012.04.005
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    References listed on IDEAS

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    1. J. C. Lee & C. H. Chang, 2000. "Bayesian Analysis of a Growth Curve Model with a General Autoregressive Covariance Structure," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 703-713, December.
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    4. Anuradha Roy, 2008. "Computation aspects of the parameter estimates of linear mixed effects model in multivariate repeated measures set-up," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(3), pages 307-320.
    5. Lu, Nelson & Zimmerman, Dale L., 2005. "The likelihood ratio test for a separable covariance matrix," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 449-457, July.
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    7. Hao Wang & Mike West, 2009. "Bayesian analysis of matrix normal graphical models," Biometrika, Biometrika Trust, vol. 96(4), pages 821-834.
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    Cited by:

    1. Monica Billio & Roberto Casarin & Matteo Iacopini & Sylvia Kaufmann, 2023. "Bayesian Dynamic Tensor Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(2), pages 429-439, April.
    2. Salvatore D. Tomarchio & Paul D. McNicholas & Antonio Punzo, 2021. "Matrix Normal Cluster-Weighted Models," Journal of Classification, Springer;The Classification Society, vol. 38(3), pages 556-575, October.
    3. Ivan Žežula & Daniel Klein & Anuradha Roy, 2018. "Testing of multivariate repeated measures data with block exchangeable covariance structure," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 360-378, June.
    4. Lingzhe Guo & Reza Modarres, 2020. "Testing the equality of matrix distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(2), pages 289-307, June.
    5. Federico Ferraccioli & Giovanna Menardi, 2023. "Modal clustering of matrix-variate data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(2), pages 323-345, June.
    6. Volodymyr Melnykov & Xuwen Zhu, 2019. "Studying crime trends in the USA over the years 2000–2012," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(1), pages 325-341, March.
    7. Timothy Opheim & Anuradha Roy, 2021. "Linear models for multivariate repeated measures data with block exchangeable covariance structure," Computational Statistics, Springer, vol. 36(3), pages 1931-1963, September.

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