Collapsibility for directed acyclic graphs

Scandinavian Journal of Statistics

Volumn 36, Issue 2, 2009, Pages 185-203

  Xie, Xianchao ^a   Geng, Zhi ^a  

^a PEKING UNIVERSITY   (China)

Author keywords

Directed acyclic graph; Graphical model; Model collapsibility

Indexed keywords

EID: 67949118802     PISSN: 03036898     EISSN: 14679469     Source Type: Journal    
DOI: 10.1111/j.1467-9469.2008.00627.x     Document Type: Article

References (22)

1. Asmussen, S. & Edwards, D. (1983). Collapsibility and response variables in contingency tables. Biometrika 70, 567-578.
2. Cox, D. R. & Wermuth, N. (2003). A general condition for avoiding effect reversal after marginalization. J. Roy. Statist. Soc. Ser. B 65, 937-941.
3. Didelez, V. & Edwards, D. (2004). Collapsibility of graphical CG-regression models. Scand. J Statist. 31, 535-551.
4. Ducharme, G. R. & Lepage, Y. (1986). Testing collapsibility in contingency tables. J. Roy. Statist. Soc. Ser. B 48, 197-205.
5. Fraser, D. A. S. (1956). Sufficient statistics with nuisance parameters. Ann. Math. Statist. 27, 838-842.
6. Frydenberg, M. (1990). Marginalization and collapsibility in graphical interaction models. Ann. Statist. 18, 790-805.
7. Geng, Z. (1992). Collapsibility of relative risks in contingency tables with a response variable. J. Roy. Statist. Soc. Ser. B 54, 585-593.
8. Kim, S. H. & Kim, S. H. (2006). A note on collapsibility in DAG models of contingency tables. Scand. J. Statist. 33, 575-590.
9. Lauritzen, S. L. (1996). Graphical models. Clarendon Press, Oxford.
10. Madigan, D. & Mosurski, K. (1990). An extension of the results of Asmussen and Edwards on collapsibility in contingency tables. Biometrika 77, 315-319.
11. Meek, C. (1995). Strong completeness and faithfulness in Bayesian networks. In Proceedings of the 11th Conference on Uncertainty in Artificial Intelligence, 411-418. Morgan Kaufmann, Montreal.
12. Pearl, J. (1988). Probabilistic reasoning in intelligent systems. Morgan Kaufmann, San Fransisco, CA.
13. Pearl, J. (2000). Causality. Cambridge University Press, Cambridge.
14. Richardson, T. & Spirtes, P. (2002). Ancestral graph Markov models. Ann., Statist. 30, 962-1030.
15. Simpson, E. H. (1951). The interpretation of interaction in contingency tables. J. Roy. Statist. Soc. Ser. B 13, 238-241.
16. Spirtes, P., Glymour, C. & Scheines, R. (1993). Causation, prediction and search. Springer-Verlag, New York.
17. Verma, T. & Pearl, J. (1990a). Causal networks: semantics and expressiveness. In Proceedings of the 4th Conference on Uncertainty in Artificial Intelligence, 69-78. Elsevier, Amsterdam..
18. Verma, T. & Pearl, J. (1.990b). Equivalence and synthesis of causal models. In Proceedings of the 6th Conference on Uncertainty in Artificial Intelligence, 255-268. Elsevier, Amsterdam..
19. Wermuth, N. (1987). Parametric collapsibility and the lack, of moderating effects in contingency tables with a dichotomous response variable. J. Roy. Statist. Soc. Ser. B 49, 353-364.
20. Whittaker, J. (1990). Graphical models in applied multivariate statistics. John Wiley & Sons, New York.
21. Whittemore, A. S. (1978). Collapsibility of multidimensional contingency tables. J. Roy. Statist. Soc. Ser. B 40, 328-340.
22. Yule, G. U. (1.903). Notes on the theory of association of attributes in statistics. Biometrika 2, 121134.