Mixed graphical association models; discussions and reply

On donne une vue d'ensemble de la theorie mathematique et statistique des modeles d'association graphiques mixtes, concernes par la description d'associations entre variables, ou certaines sont admises etre quantitatives et d'autres qualitatives. Tous ces modeles (ayant ses origines en particulier en physique statistique et en genetique) sont determines par des restrictions de type distributionnel complete par des restrictions d'independance conditionnelle. Ils elargissent et unifient un certain nombre de techniques statistiques qui sont bien etablies, surtout en sciences sociales. L'article est suivi de discussions et de commentaires

[1]  S. Wright.  The Method of Path Coefficients , 1934 .

[2]  K. Wagner.  Über eine Eigenschaft der ebenen Komplexe , 1937 .

[3]  H. Wold.  Causality and Econometrics , 1954 .

[4]  G. Dirac.  On rigid circuit graphs , 1961 .

[5]  N. N. Vorob’ev.  Consistent Families of Measures and Their Extensions , 1962 .

[6]  N. N. Vorob’ev.  Markov Measures and Markov Extensions , 1963 .

[7]  M. W. Birch.  Maximum Likelihood in Three-Way Contingency Tables , 1963 .

[8]  H. Kellerer.  Verteilungsfunktionen mit gegebenen Marginalverteilungen , 1964 .

[9]  A. Goldberger,et al.  Causal Models in the Social Sciences. , 1972 .

[10]  J. Darroch,et al.  Generalized Iterative Scaling for Log-Linear Models , 1972 .

[11]  S. Haberman,et al.  The analysis of frequency data , 1974 .

[12]  N. Wermuth.  Model Search among Multiplicative Models , 1976 .

[13]  David Williams,et al.  Improved likelihood ratio tests for complete contingency tables , 1976 .

[14]  A. Dawid.  Conditional Independence in Statistical Theory , 1979 .

[15]  A. Dawid.  Conditional Independence for Statistical Operations , 1980 .

[16]  N. Wermuth.  Linear Recursive Equations, Covariance Selection, and Path Analysis , 1980 .

[17]  M. Golumbic.  Algorithmic graph theory and perfect graphs , 1980 .

[18]  Catriel Beeri,et al.  Properties of acyclic database schemes , 1981, STOC '81.

[19]  D. A. Kenny,et al.  Correlation and Causation , 1937, Wilmott.

[20]  Joe Whittaker,et al.  Glim Syntax and Simultaneous Tests for Graphical Log Linear Models , 1982 .

[21]  T. Speed,et al.  Structural Analysis of Multivariate Data: A Review , 1982 .

[22]  David F. Hendry,et al.  The Econometric-analysis of Economic Time-series , 1983 .

[23]  D. Edwards,et al.  The analysis of contingency tables by graphical models , 1983 .

[24]  Catriel Beeri,et al.  On the Desirability of Acyclic Database Schemes , 1983, JACM.

[25]  T. Speed,et al.  Additive and Multiplicative Models and Interactions , 1983 .

[26]  T. Speed,et al.  Recursive causal models , 1984, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[27]  T. Speed,et al.  Decomposable graphs and hypergraphs , 1984, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[28]  M. Browne.  Asymptotically distribution-free methods for the analysis of covariance structures. , 1984, The British journal of mathematical and statistical psychology.

[29]  B. T. Porteous,et al.  Improved likelihood ratio statistics for covariance selection models , 1985 .

[30]  T. Speed,et al.  Gaussian Markov Distributions over Finite Graphs , 1986 .

[31]  D. Edwards,et al.  A fast model selection procedure for large families of models , 1987 .

[32]  Reinhard Diestel.  Simplicial decompositions of graphs - Some uniqueness results , 1987, J. Comb. Theory, Ser. B.

[33]  Judea Pearl,et al.  The Logic of Representing Dependencies by Directed Graphs , 1987, AAAI.

[34]  K. Jöreskog.  Analysis of Covariance Structures , 1988 .

[35]  H.-G. Leimer.  Triangulated Graphs with Marked Vertices , 1988 .

[36]  J. Q. Smith.  Influence Diagrams for Statistical Modelling , 1989 .

[37]  B. T. Porteous.  Stochastic Inequalities Relating a Class of Log-Likelihood Ratio Statistics to their Asymptotic $\chi^2$ Distribution , 1989 .

[38]  M. Frydenberg.  The chain graph Markov property , 1990 .