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On the Validity of the Markov Interpretation of Path Diagrams of Gaussian Structural Equations Systems with Correlated Errors

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  • Jan T. A. Koster

Abstract

Pearl's d‐separation concept and the ensuing Markov property is applied to graphs which may have, between each two different vertices i and j, any subset of {i←j, i→j, i↔j} as edges. The class of graphs so obtained is closed under marginalization. Furthermore, the approach permits a direct proof of this theorem: “The distribution of a multivariate normal random vector satisfying a system of linear simultaneous equations is Markov w.r.t. the path diagram of the linear system”.

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  • Jan T. A. Koster, 1999. "On the Validity of the Markov Interpretation of Path Diagrams of Gaussian Structural Equations Systems with Correlated Errors," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(3), pages 413-431, September.
    • Handle: RePEc:bla:scjsta:v:26:y:1999:i:3:p:413-431
    DOI: 10.1111/1467-9469.00157
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    Cited by:

    1. Riccardo Borgoni & Ann Berrington & Peter Smith, 2012. "Selecting and fitting graphical chain models to longitudinal data," Quality & Quantity: International Journal of Methodology, Springer, vol. 46(3), pages 715-738, April.
    2. Colombi, R. & Giordano, S., 2012. "Graphical models for multivariate Markov chains," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 90-103.
    3. Ying-Chao Hung & Neng-Fang Tseng, 2013. "Extracting informative variables in the validation of two-group causal relationship," Computational Statistics, Springer, vol. 28(3), pages 1151-1167, June.

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