Computing Statistically-Equivalent Path Models
Path model from covariance matrix with ordering
Return parent indices from a (weighted) DAG for a given child
Calculate residual-covariance matrix based on a path model and covaria...
Path model from ordered precision matrix
SE-set from precision matrix
Generate all topological orderings
Precision matrix from ordered path model
Edge frequency in the SE-set
Compute Controllability Distribution in the SE-set
Re-order rows and columns
Precision matrices from the SEset
Tools to compute and analyze the set of statistically-equivalent (Gaussian, linear) path models which generate the input precision or (partial) correlation matrix. This procedure is useful for understanding how statistical network models such as the Gaussian Graphical Model (GGM) perform as causal discovery tools. The statistical-equivalence set of a given GGM expresses the uncertainty we have about the sign, size and direction of directed relationships based on the weights matrix of the GGM alone. The derivation of the equivalence set and its use for understanding GGMs as causal discovery tools is described by Ryan, O., Bringmann, L.F., & Schuurman, N.K. (2022) <doi: 10.31234/osf.io/ryg69>.