Statistics – Methodology
Scientific paper
2011-10-10
Statistics
Methodology
30 pages, 7 figures, 2 tables
Scientific paper
In this paper, we study sequences of regressions in joint or single responses given a set of context variables, where a dependence structure of interest is captured by a regression graph. These graphs have nodes representing random variables and three types of edge. Their set of missing edges defines the independence structure of the graph provided two properties are used that are not common to all probability distributions, named the intersection and the composition property. We derive the additionally needed properties for tracing the effects of single active paths and for excluding any canceling of effects due to several paths connecting the same pair of nodes. For this, we use the notion of a generating process for the joint distribution and derive new properties of an edge matrix calculus for transforming graphs. One key is the M-matrix property of each regularized square edge matrix, others are the proposed notions of traceable regressions and of singleton transitivity.
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