Likelihood factorizations for mixed discrete and continuous variables

Scandinavian Journal of Statistics

Volumn 26, Issue 2, 1999, Pages 209-220

  Cox, D R ^a   Wermuth, Nanny ^b  

^a NUFFIELD COLLEGE   (United Kingdom)

^b Ctr of Surv Res and Methodol   (Germany)

Author keywords

Conditional Gaussian model; Conditional independence; Graph; Likelihood; Median dichotomized Gaussian distribution; Multivariate normal distribution; Partially dichotomized Gaussian model; Prime graph; Separation theorem

Indexed keywords

EID: 0033241920     PISSN: 03036898     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9469.00145     Document Type: Article

References (22)

1. Azzalini, A. & Dalla Valle, A. (1996). The multivariate skew-normal distribution. Biometrika 83, 715-726.
2. Barndorff-Nielsen, O. E. (1978). Information and exponential families. Wiley, Chichester.
3. Bollen, K. A. (1989). Structural equations with latent variables. Wiley, New York.
4. Cox, D. R. & Reid, N. (1987). Parameter orthogonality and approximate conditional inference (with discussion). J. Roy. Statist. Soc. Ser. B 49, 1 -39.
5. Cox, D. R. & Wermuth, N. (1992). Response models for mixed binary and quantitative variables. Biometrika 79, 441-461.
6. Cox, D. R. & Wermuth, N. (1993). Linear dependencies represented by chain graphs (with discussion). Statist. Sci. 8, 204-283.
7. Cox, D. R. & Wermuth, N. (1996). Multivariate dependencies: models, analysis and interpretation. Chapman & Hall, London.
8. Darroch, J. N., Lauritzen, S. L. & Speed, T. P. (1980). Markov fields and log-linear models for contingency tables. Ann. Statist. 8, 522-539.
9. Dempster, A. P. (1972). Covariance selection. Biometrics 28, 157-175.
10. Edwards, D. ( 1995). Introduction to graphical modelling. Oxford University Press, Oxford.
11. Frydenberg, M. (1990). Marginalization and collapsibility in graphical interaction models. Ann. Statist. 18, 790-805.
12. Frydenberg, M. & Lauritzen, S. L. (1989). Decomposition of maximum likelihood in mixed graphical interaction models. Biometrika 76, 539-555.
13. Jöreskog, K. G. (1981). Analysis of covariance structures. Scand. J. Statist 8, 65-92.
14. Lauritzen, S. L. (1996). Graphical models. Oxford University Press, Oxford.
15. Lauritzen, S. L. & Wermuth, N. (1989). Graphical models for associations between variables, some of which are qualitative and some quantitative. Ann. Statist. 17, 31-54.
16. Leimer, H.-G. (1993). Optimal decomposition by clique separators. Discrete Math. 113, 99-123.
17. Matúš, F. (1994). On the maximum-entropy extensions of probability measures over undirected graphs. Proc. WUPES'94, pp. 181-198. Institute of Information Theory and Automation, Trest.
18. Wermuth, N. (1976). Analogies between multiplicative models in contingency tables and covariance selection. Biometrics 32, 95-108.
19. Wermuth, N. (1980). Linear recursive equations, covariance selection, and path analysis. J. Amer. Statist. Assoc. 75, 963-997.
20. Wermuth, N. (1998). Graphical Markov models. In Encyclopedia of statistical sciences (eds S. Kotz, C. Read & D. Banks) update vol. 2, 284-300. Wiley, New York.
21. Wermuth, N. & Cox, D. R. (1998). On association models defined over independence graphs. Bernoulli (to appear).
22. Wermuth, N. & Lauritzen, S. L. (1983). Graphical and recursive models for contingency tables. Biometrika 70, 537-552.