Marginal log-linear parameterization of conditional independence models

Biometrika

Volumn 97, Issue 4, 2010, Pages 1006-1012

  Rudas, Tamás ^a   Bergsma, Wicher P ^b   Németh, Renáta ^a  

^a EÖTVÖS LORÁND UNIVERSITY   (Hungary)

^b LONDON SCHOOL OF ECONOMICS   (United Kingdom)

Author keywords

Chain graph; Conditional independence; Graphical model; Marginal model; Smoothness

Indexed keywords

EID: 78651275164     PISSN: 00063444     EISSN: 14643510     Source Type: Journal    
DOI: 10.1093/biomet/asq037     Document Type: Article

References (22)

1. AGRESTI, A. (2002). Categorical Data Analysis, 2nd ed. New York: Wiley.
2. ANDERSSON, S. A., MADIGAN, D. & PERLMAN, M. D. (2001). Alternative Markov properties for chain graphs. Scand. J. Statist. 28, 33-85.
3. BARNDORFF-NIELSEN, O. (1978). Information and Exponential Families. New York: Wiley.
4. BERGSMA, W. P. (1997). Marginal Models for Categorical Data. Tilburg: Tilburg University Press.
5. BERGSMA, W. P., CROON, M. A. & HAGENAARS, J. A. (2009). Marginal Models for Dependent, Clustered and Longitudinal Categorical Data. New York: Springer.
6. BERGSMA, W. P. & RUDAS, T. (2002a). Marginal models for categorical data. Ann. Statist. 30, 140-59.
7. BERGSMA, W. P. & RUDAS, T. (2002b). Variation independent parameterizations of categorical distributions. In Distributions with Given Marginals and Statistical Modelling, Ed. C. M. Cuadras, J. Fortiana and J. A. Rodriguez-Lallena, pp. 21-7. Dordrecht: Kluwer.
8. BISHOP, Y. V. V., FIENBERG, S. E. & HOLLAND, P. W. (1975). Discrete Multivariate Analysis. Cambridge: MIT Press.
9. COX, D. R. & WERMUTH, N. (1996). Multivariate Dependencies. London: Chapman and Hall.
10. CSISZÁR, I. (1975). I-divergence geometry of probability distributions and minimization problems. Ann. Prob. 3, 146-58.
11. DRTON, M. (2009). Discrete chain graph models. Bernoulli 15, 736-53.
12. FRYDENBERG, M. (1990). The chain graph Markov property. Scand. J. Statist. 17, 333-53.
13. LANG, J. B. & AGRESTI, A. (1994). Simultaneously modelling the joint and marginal distributions of multivariate categorical responses. J. Am. Statist. Assoc. 89, 625-32.
14. LAURITZEN, S. L. (1996). Graphical Models. Oxford: Clarendon Press.
15. LAURITZEN, S. L., DAWID, A. P., LARSEN, B. N. & LEIMER, H. G. (1990). Independence properties of directed Markov fields. Networks 20, 491-505.
16. LAURITZEN, S. L. & WERMUTH, N. (1989). Graphical models for associations between variables, some of which are qualitative and some quantitative. Ann. Statist. 17, 31-57.
17. MARCHETTI, G. L. & LUPPARELLI, M. (2008). Parameterization and fitting of a class of discrete graphical models. In COMPSTAT 2008, Proc. Comp. Statist., Ed. P. Brito, pp. 117-28. Heidelberg: Physica.
18. RICHARDSON, T. (2003). Markov properties for acyclic directed mixed graphs. Scand. J. Statist. 30, 145-57.
19. RUDAS, T. (1998). Odds Ratios in the Analysis of Contingency Tables. Newbury Park: Sage.
20. RUDAS, T., BERGSMA, W. P. & NÉMETH, R. (2006). Parameterization and estimation of path models for categorical data. In COMPSTAT 2006, Proc. Comp. Statist., Ed. A. Rizzi and M. Vichi, pp. 383-94. Heidelberg: Physica.
21. STUDENY, M. (2005). Probabilistic Conditional Independence Structures. New York: Springer.
22. WERMUTH, N. & COX, D. R. (2004). Joint response graphs and separation induced by triangular systems. J. R. Statist. Soc. B 66, 687-717.