Partial Inversion and Partial Closure of Paths in Graphs: Two Matrix Operators to Study Properties of Multivariate Dependencies

Abstract

Graphical Markov models have some advantages over other multivariate statitical models. They permit to model stepwise data generating processes with and without interventions and to work out consequences of a large model for subsets of variables. Such implications can then be compared with available background knowledge or may be used to judge seemingly inconsistent results in similar studies. Two recently developed matrix operators, one for real-valued matrices and one for binary matrices are useful for understanding and deriving properties and implications of graphical Markov models.