IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v66y1998i2p133-187.html
   My bibliography  Save this article

Normal Linear Regression Models With Recursive Graphical Markov Structure

Author

Listed:
  • Andersson, Steen A.
  • Perlman, Michael D.

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.

Suggested Citation

  • Andersson, Steen A. & Perlman, Michael D., 1998. "Normal Linear Regression Models With Recursive Graphical Markov Structure," Journal of Multivariate Analysis, Elsevier, vol. 66(2), pages 133-187, August.
  • Handle: RePEc:eee:jmvana:v:66:y:1998:i:2:p:133-187
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(98)91745-6
    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. Andersson, S. A. & Perlman, M. D., 1995. "Testing Lattice Conditional Independence Models," Journal of Multivariate Analysis, Elsevier, vol. 53(1), pages 18-38, April.
    2. Ross D. Shachter & C. Robert Kenley, 1989. "Gaussian Influence Diagrams," Management Science, INFORMS, vol. 35(5), pages 527-550, May.
    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.
    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. Katarzyna Filipiak & Dietrich Rosen, 2012. "On MLEs in an extended multivariate linear growth curve model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(8), pages 1069-1092, November.
    2. Andersson, Steen A. & Klein, Thomas, 2010. "On Riesz and Wishart distributions associated with decomposable undirected graphs," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 789-810, April.
    3. 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.

    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:jmvana:v:66:y:1998:i:2:p:133-187. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.