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Algebraic Descriptions of Nominal Multivariate Discrete Data

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  • Teugels, J. L.
  • Van Horebeek, J.

Abstract

Traditionally, multivariate discrete data are analyzed by means of log-linear models. In this paper we show how an algebraic approach leads naturally to alternative models, parametrized in terms of the moments of the distribution. Moreover we derive a complete characterization of all meaningful transformations of the components and show how transformations affect the moments of a distribution. It turns out that our models provide the necessary formal description of longitudinal data; moreover in the classical case, they can be considered as an analysis tool, complementary to log-linear models.

Suggested Citation

  • Teugels, J. L. & Van Horebeek, J., 1998. "Algebraic Descriptions of Nominal Multivariate Discrete Data," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 203-226, November.
    • Handle: RePEc:eee:jmvana:v:67:y:1998:i:2:p:203-226
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    References listed on IDEAS

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    1. Teugels, Jozef L, 1990. "Some representations of the multivariate Bernoulli and binomial distributions," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 256-268, February.
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    Cited by:

    1. Anders Ekholm & Jukka Jokinen & John W. McDonald & Peter W. F. Smith, 2003. "Joint Regression and Association Modeling of Longitudinal Ordinal Data," Biometrics, The International Biometric Society, vol. 59(4), pages 795-803, December.
    2. Ip, Edward H. & Wang, Yuchung J. & Yeh, Yeong-nan, 2004. "Structural decompositions of multivariate distributions with applications in moment and cumulant," Journal of Multivariate Analysis, Elsevier, vol. 89(1), pages 119-134, April.
    3. Jokinen, Jukka, 2006. "Fast estimation algorithm for likelihood-based analysis of repeated categorical responses," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1509-1522, December.

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