A Unified Theory of Causal Models
Harri Kiiveri · Bulletin of the Australian Mathematical Society · 1984
Directed graphs and conditional independence ideas are used to define a class of causal models applicable to a finite set of random variables.Given the directed graph for a particular model, a factorization of the joint distribution of the random variables can be written down and rules given for reading the conditional independence relations amongst the variables.The definition does not depend on any particular distributional form and hence can be applied to models with both discrete and continuous random variables.However, the most tractable examples are those for which the joint distribution is normal, or a product of multinomials, and these are considered in detail.In the normal case connections are demonstrated with covariance selection, structural equation models, and the analysis of covariance structures as considered by Joreskog [4], McDonald [5] and others.Topics covered include variance components, path analysis, factor analysis and regression with errors in variables.Discrete counterparts of the recursive models in the normal case are obvious from the general definition and these are shown to include models considered by Goodman [2] and Haberman [3].Examples covered include latent structure analysis and contingency tables with ordered variables.Models containing unobserved or latent variables are treated using theory for incomplete data.This results in a more compact parameterization