Parameterization and fitting of a class of discrete graphical models

COMPSTAT 2008 - Proceedings in Computational Statistics, 18th Symposium

Volumn , Issue , 2008, Pages 117-128

  Marchetti, Giovanni M ^a   Lupparelli, Monia ^b  

^a UNIVERSITY OF FLORENCE   (Italy)

^b UNIVERSITY OF PAVIA   (Italy)

Author keywords

Bi directed graphs; Complete hierarchical parameterizations; Covariance graphs; Multivariate regression chain graphs; Reduced model estimates

Indexed keywords

DIRECTED GRAPHS; ITERATIVE METHODS; MARKOV PROCESSES; MAXIMUM LIKELIHOOD; MULTIVARIANT ANALYSIS; PARAMETERIZATION; REGRESSION ANALYSIS; SURVEYS;

CHAIN GRAPH; COMPLETE HIERARCHICAL PARAMETERIZATIONS; CONDITIONAL INDEPENDENCES; COVARIANCE GRAPHS; ITERATIVE GRADIENT-BASED ALGORITHMS; LINEAR PARAMETERIZATIONS; MULTIVARIATE STATISTICAL MODELS; REDUCED MODEL;

PARAMETER ESTIMATION;

EID: 68949096088     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/978-3-7908-2084-3_10     Document Type: Conference Paper

References (21)

1. AITCHISON, J. and SILVEY, S.D. (1958): Maximum likelihood estimation of parameter subject to restraints. Annals of Mathematical Statistics 29, 813-828.
2. BARTOLUCCI, F., COLOMBI, R. and FORCINA, A. (2007): An extended class of marginal link functions for modelling contingency tables by equality and inequality constraints. Statistica Sinica 17, 691-711.
3. BERGSMA, W.P. (1997): Marginal models for categorical data, Ph.D Thesis, Tilburg.
4. BERGSMA, W.P. and RUDAS, T. (2002): Marginal log-linear models for categorical data. Annals of Statistics 30, 140-159.
5. COX, D.R. (2006): Principles of Statistical Inference. Cambridge University Press, Cambridge.
6. COX, D.R. and WERMUTH, N. (1990): An approximation to maximum likelihood estimates in reduced models. Biometrika 77, 747-761.
7. COX, D.R. and WERMUTH, N. (1996): Multivariate dependencies. Models, analysis and interpretation. Chapman and Hall, London.
8. DAVIS, J.A., SMITH, T.W. and MARDSEN, J.A. (2007): General Social Surveys Cumulative Codebook: 1972-2006. NORC, Chicago. URL http://sda.berkeley.edu/GSS/ .
9. DRTON, M., EICHLER, M. and RICHARDSON, T.S. (2007): Identification and Likelihood Inference for Recursive Linear Models with Correlated Errors. arXiv:0601631.
10. DRTON, M. and RICHARDSON, T.S. (2008): Binary models for marginal independence, J. Royal Statist. Soc., Ser. B 70, 287-309.
11. GLONEK, G.F.V. and McCULLAGH, P. (1995): Multivariate logistic models. J. Royal Statist. Soc., Ser. B 57, 533-546.
12. KAUERMANN, G. (1996): On a dualization of graphical Gaussian models. Scand. J. of Statistics 23, 105-116.
13. KAUERMANN, G. (1997): A note on multivariate logistic models for contingency tables. Australian Journal of Statistics 39(3), 261-276.
14. LAURITZEN, S.L. (1996): Graphical Models. Oxford University Press, Oxford.
15. LUPPARELLI, M., MARCHETTI, G.M. and BERGSMA, W.P. (2008): Parameterizations and fitting of bi-directed graph models to categorical data. arXiv:0801.1440.
16. R DEVELOPMENT CORE TEAM (2008): R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org.
17. RICHARDSON, T.S. (2003): Markov property for acyclic directed mixed graphs, Scand. J. of Statistics 30, 145-157.
18. RODDAM, A.W. (2004): An approximate maximum likelihood procedure for parameter estimation in multivariate discrete data regression models. J. of Applied Statistics 28, 273-279.
19. RUDAS, T., BERGSMA, W.P. and NÉMETH, R. (2006): Parameterization and estimation of path models for categorical data. In: A. Rizzi & M. Vichi, (Eds.): Compstat 2006 Proceedings. Physica-Verlag, Heidelberg, 383-394.
20. WERMUTH, N. and COX, D.R. (2004): Joint response graphs and separation induced by triangular systems. J. Royal Statist. Soc. B 66, 687-717.
21. WERMUTH, N., COX, D.R. and MARCHETTI, G.M. (2006): Covariance chains. Bernoulli, 12, 841-862.