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Collapsibility for Directed Acyclic Graphs

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  • XIANCHAO XIE
  • ZHI GENG

Abstract

. Collapsibility means that the same statistical result of interest can be obtained before and after marginalization over some variables. In this paper, we discuss three kinds of collapsibility for directed acyclic graphs (DAGs): estimate collapsibility, conditional independence collapsibility and model collapsibility. Related to collapsibility, we discuss removability of variables from a DAG. We present conditions for these three different kinds of collapsibility and relationships among them. We give algorithms to find a minimum variable set containing a variable subset of interest onto which a statistical result is collapsible.

Suggested Citation

  • Xianchao Xie & Zhi Geng, 2009. "Collapsibility for Directed Acyclic Graphs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 185-203, June.
    • Handle: RePEc:bla:scjsta:v:36:y:2009:i:2:p:185-203
    DOI: 10.1111/j.1467-9469.2008.00627.x
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    References listed on IDEAS

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    1. D. R. Cox & Nanny Wermuth, 2003. "A general condition for avoiding effect reversal after marginalization," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 937-941, November.
    2. Sung‐Ho Kim & Seong‐Ho Kim, 2006. "A Note on Collapsibility in DAG Models of Contingency Tables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 575-590, September.
    3. Vanessa Didelez & David Edwards, 2004. "Collapsibility of Graphical CG‐Regression Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(4), pages 535-551, December.
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    Cited by:

    1. Heng, Pei & Sun, Yi, 2023. "Algorithms for Convex Hull Finding in Undirected Graphical Models," Applied Mathematics and Computation, Elsevier, vol. 445(C).
    2. Binghui Liu & Jianhua Guo, 2013. "Collapsibility of Conditional Graphical Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(2), pages 191-203, June.

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