I'm running PC and GES searches on multiple datasets, and I'm confused about the results in the Search box.
Sometimes each existing edge is oriented in the resulting Pattern (some edges do not exist when a pair is d-separated), while other times the Pattern contains some undirected edges, thus representing a Markov class of potential DAGs.
In the case of undirected edges, does choosing "DAG in pattern" yield the "best fitting" DAG according to TETRAD IV or is it just one of the equivalent DAGs within the Markov class? That is, would it be correct to say that a causal structure could not be determined when the pattern contains undirecte edges or is the "DAG in pattern" the correct (unique) causal structure?
Also, the "DAG in pattern" varies across PC and GES searches (I assume this should limit my confidence in either DAG being a correct unique causal representation).
If I choose "Graph" and "Global Score-based Reorientation" and then "Graph" and "Choose DAG in Pattern" then a DAG appears on the "Pattern" tab of a PC search box that is different from that in the "DAG in pattern" tab. Although the TETRAD manual says that "Global Score-based Reorientation" runs GES on the present edges, the DAG shown in the "Pattern" tab of the PC search box does not correspond to the "DAG in pattern" tab from a GES search. Moreover, if I perform the same steps in a GES search, different DAGs will appear on the "Pattern" and "DAG in pattern" tabs.
Any insights are appreciated. Thanks,
Jason