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Likelihood Factorizations for Mixed Discrete and Continuous Variables

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  • D. R. Cox
  • Nanny Wermuth

Abstract

Some general remarks are made about likelihood factorizations, distinguishing parameter‐based factorizations and concentration‐graph factorizations. Two parametric families of distributions for mixed discrete and continuous variables are discussed. Conditions on graphs are given for the circumstances under which their joint analysis can be split into separate analyses, each involving a reduced set of component variables and parameters. The result shows marked differences between the two families although both involve the same necessary condition on prime graphs. This condition is both necessary and sufficient for simplified estimation in Gaussian and for discrete log linear models.

Suggested Citation

  • D. R. Cox & Nanny Wermuth, 1999. "Likelihood Factorizations for Mixed Discrete and Continuous Variables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(2), pages 209-220, June.
    • Handle: RePEc:bla:scjsta:v:26:y:1999:i:2:p:209-220
    DOI: 10.1111/1467-9469.00145
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    Cited by:

    1. Nanny Wermuth & Kayvan Sadeghi, 2012. "Sequences of regressions and their independences," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 215-252, June.
    2. Robins, James M., 2003. "General methodological considerations," Journal of Econometrics, Elsevier, vol. 112(1), pages 89-106, January.
    3. Fentaw Abegaz & Ernst Wit, 2015. "Copula Gaussian graphical models with penalized ascent Monte Carlo EM algorithm," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(4), pages 419-441, November.
    4. Konno, Yoshihiko, 2001. "Inadmissibility of the Maximum Likekihood Estimator of Normal Covariance Matrices with the Lattice Conditional Independence," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 33-51, October.

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