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Normal Linear Regression Models With Recursive Graphical Markov Structure

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  • Andersson, Steen A.
  • Perlman, Michael D.
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    Abstract

    A multivariate normal statistical model defined by the Markov properties determined by an acyclic digraph admits a recursive factorization of its likelihood function (LF) into the product of conditional LFs, each factor having the form of a classical multivariate linear regression model ([reverse not equivalent]WMANOVA model). Here these models are extended in a natural way to normal linear regression models whose LFs continue to admit such recursive factorizations, from which maximum likelihood estimators and likelihood ratio (LR) test statistics can be derived by classical linear methods. The central distribution of the LR test statistic for testing one such multivariate normal linear regression model against another is derived, and the relation of these regression models to block-recursive normal linear systems is established. It is shown how a collection of nonnested dependent normal linear regression models ([reverse not equivalent]Wseemingly unrelated regressions) can be combined into a single multivariate normal linear regression model by imposing a parsimonious set of graphical Markov ([reverse not equivalent]Wconditional independence) restrictions.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 66 (1998)
    Issue (Month): 2 (August)
    Pages: 133-187

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    Handle: RePEc:eee:jmvana:v:66:y:1998:i:2:p:133-187

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    Related research

    Keywords: multivariate normal distribution multivariate analysis of variance (MANOVA) linear regression recursive linear models directed graph graphical Markov model conditional independence maximum likelihood estimate likelihood ratio test seemingly unrelated regressions;

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Ross D. Shachter & C. Robert Kenley, 1989. "Gaussian Influence Diagrams," Management Science, INFORMS, vol. 35(5), pages 527-550, May.
    2. Andersson, S. A. & Perlman, M. D., 1995. "Testing Lattice Conditional Independence Models," Journal of Multivariate Analysis, Elsevier, vol. 53(1), pages 18-38, April.
    3. Andersson, S. A. & Perlman, M. D., 1995. "Unbiasedness of the Likelihood Ratio Test for Lattice Conditional Independence Models," Journal of Multivariate Analysis, Elsevier, vol. 53(1), pages 1-17, April.
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    Cited by:
    1. Katarzyna Filipiak & Dietrich Rosen, 2012. "On MLEs in an extended multivariate linear growth curve model," Metrika, Springer, vol. 75(8), pages 1069-1092, November.
    2. Drton, Mathias & Andersson, Steen A. & Perlman, Michael D., 2006. "Conditional independence models for seemingly unrelated regressions with incomplete data," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 385-411, February.

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