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Collapsibility of Graphical CG‐Regression Models

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  • Vanessa Didelez
  • David Edwards

Abstract

. CG‐regressions are multivariate regression models for mixed continuous and discrete responses that result from conditioning in the class of conditional Gaussian (CG) models. Their conditional independence structure can be read off a marked graph. The property of collapsibility, in this context, means that the multivariate CG‐regression can be decomposed into lower dimensional regressions that are still CG and are consistent with the corresponding subgraphs. We derive conditions for this property that can easily be checked on the graph, and indicate computational advantages of this kind of collapsibility. Further, a simple graphical condition is given for checking whether a decomposition into univariate regressions is possible.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:31:y:2004:i:4:p:535-551
    DOI: 10.1111/j.1467-9469.2004.00405.x
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    Cited by:

    1. 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.
    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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