Directed cyclic graphs, conditional independence, and non-recursive linear structural equation models

Abstract: "Recursive linear structural equation models can be represented by directed acyclic graphs. When represented in this way, they satisfy the Markov Condition. Hence it is possible to use the graphical d-separation to determine what conditional independence relations are entailed by a given linear structural equation model. I prove in this paper that it is also possible to use the graphical d-separation applied to a cyclic graph to determine what conditional independence relations are entailed to hold by a given non-recursive linear structural equation model. I also give a causal intepretation to the linear coefficients in a non- recursive structural equation models, and explore the relationships between cyclic graphs and undirected graphs, directed acyclic graphs with latent variables, and chain independence graphs."