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A general condition for avoiding effect reversal after marginalization

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  • D. R. Cox
  • Nanny Wermuth

Abstract

Summary. The paper examines the effect of marginalizing over a possibly unobserved background variable on the conditional relation between a response and an explanatory variable. In particular it is shown that some conclusions derived from least squares regression theory apply in general to testing independence for arbitrary distributions. It is also shown that the general condition of independence of the explanatory variable and the background ensures that mono‐ tonicity of dependence is preserved after marginalization. Relations with effect reversal and with collapsibility are sketched.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssb:v:65:y:2003:i:4:p:937-941
    DOI: 10.1111/1467-9868.00424
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    Cited by:

    1. P. Vellaisamy, 2017. "Collapsibility of some association measures and survival models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 1155-1176, October.
    2. Nanny Wermuth & Kayvan Sadeghi, 2012. "Sequences of regressions and their independences," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 215-252, June.
    3. Hua Chen & Zhi Geng & Jinzhu Jia, 2007. "Criteria for surrogate end points," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 919-932, November.
    4. P. Vellaisamy & V. Vijay, 2007. "Some collapsibility results for n-dimensional contingency tables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(3), pages 557-576, September.
    5. 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.
    6. Wang, David Han-Min, 2010. "Corporate investment, financing, and dividend policies in the high-tech industry," Journal of Business Research, Elsevier, vol. 63(5), pages 486-489, May.
    7. Tyler J. VanderWeele & James M. Robins, 2010. "Signed directed acyclic graphs for causal inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 111-127, January.
    8. Vassilios Bazinas & Bent Nielsen, 2022. "Causal Transmission in Reduced-Form Models," Econometrics, MDPI, vol. 10(2), pages 1-25, March.

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