Linear Dependencies Represented by Chain Graphs

Various special linear structures connected with covariance matrices are reviewed and graphical methods for their representation introduced, involving in particular two different kinds of edge between the nodes representing the component variables. The distinction between decomposable and nondecomposable structures is emphasized. Empirical examples are described for the main possibilities with four component variables.

[1]  S. Wright,et al.  The Theory of Path Coefficients a Reply to Niles's Criticism. , 1923, Genetics.

[2]  Jan Tinbergen,et al.  An econometric approach to business cycle problems , 1938 .

[3]  T. Haavelmo.  The Statistical Implications of a System of Simultaneous Equations , 1943 .

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

[5]  A. Zellner.  An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias , 1962 .

[6]  Otis Dudley Duncan,et al.  Some linear models for two-wave, two-variable panel analysis. , 1969 .

[7]  K. Jöreskog.  A General Method for Estimating a Linear Structural Equation System. , 1970 .

[8]  C. Spielberger,et al.  Manual for the State-Trait Anxiety Inventory , 1970 .

[9]  D. Amick,et al.  Introduction to multivariate analysis for the social sciences , 1973 .

[10]  A. Schell,et al.  Individual differences in orienting, conditionability, and skin resistance responsivity. , 1971, Psychophysiology.

[11]  T. W. Anderson.  Asymptotically Efficient Estimation of Covariance Matrices with Linear Structure , 1973 .

[12]  D. Cox,et al.  The Choice of Variables in Observational Studies , 1974 .

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

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

[15]  V. Isham.  An Introduction to Spatial Point Processes and Markov Random Fields , 1981 .

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

[17]  N. Wermuth,et al.  Decomposable Models: A New Look at Interdependence and Dependence Structures in Psychological Research. , 1983, Multivariate behavioral research.

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

[19]  N. Wermuth,et al.  Graphical Models for Associations between Variables, some of which are Qualitative and some Quantitative , 1989 .

[20]  M. Frydenberg,et al.  A modified iterative proportional scaling algorithm for estimation for in regular exponential families , 1989 .

[21]  Kevin T. Kelly,et al.  Discovering Causal Structure. , 1989 .

[22]  M. Frydenberg,et al.  Decomposition of maximum likelihood in mixed graphical interaction models , 1989 .

[23]  S. Lauritzen,et al.  Mixed graphical association models; discussions and reply , 1989 .

[24]  J. N. R. Jeffers,et al.  Graphical Models in Applied Multivariate Statistics. , 1990 .

[25]  M. Frydenberg.  Marginalization and Collapsibility in Graphical Interaction Models , 1990 .

[26]  Nanny Wermuth,et al.  An approximation to maximum likelihood estimates in reduced models , 1990 .

[27]  N. Wermuth,et al.  On Substantive Research Hypotheses, Conditional Independence Graphs and Graphical Chain Models , 1990 .

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

[29]  Steffen L. Lauritzen,et al.  Independence properties of directed markov fields , 1990, Networks.

[30]  Judea Pearl,et al.  A Theory of Inferred Causation , 1991, KR.

[31]  S. Lauritzen,et al.  Globally convergent algorithms for maximizing a likelihood function , 1991 .

[32]  Nanny Wermuth,et al.  Graphical Models for Dependencies and Associations , 1992 .

[33]  D. Cox.  Causality : some statistical aspects , 1992 .

[34]  N. Wermuth,et al.  On the calculation of derived variables in the analysis of multivariate responses , 1992 .

[35]  Judea Pearl,et al.  An Algorithm for Deciding if a Set of Observed Independencies Has a Causal Explanation , 1992, UAI.

[36]  Nanny Wermuth,et al.  Response models for mixed binary and quantitative variables , 1992 .

[37]  Peter M. Bentler,et al.  Structural equation models with continuous and polytomous variables , 1992 .