Clustering variables in causal graphs reduces the size of the graph and simplifies causal inference. However, arbitrary clustering can alter crucial causal relations among variables and lead to erroneous conclusions. While the identifiability of a causal effect in the clustered graph implies the identifiability in the original graph under mild conditions, nonidentifiability in clustered graph does not imply nonidentifiability in the original graph without further assumptions. When both identifiability and nonidentifiability are preserved, the clustering operation is called identification invariant. We present a broad class of clustering operations that are identification invariant based on conditions related to the c-components of the original graph. Finally, we demonstrate use of the results in practical settings.
Figures & tables
Figure 1: Examples of clustering operations with undesired side effects.
Figure 2: Examples of coherent clusters ( Definition 14 ).
Figure 3: Various causal graphs that demonstrate under which conditions universal identification invariance of the clustering operation holds (green), but also when this property is lost (red).
Figure 4: Examples of clusters (marked in green) for which the corresponding clustering operation is universally identification invariant, but none of the clusters is plain, c-coherent or c-isolated.
Figure 5: Graphs modeling how different factors affect sleep medication use (adapted from ( evandt07noise ) , additional bidirected arcs included). Color-coding is applied to highlight different clusters of interest: Vertices belonging to the cluster T1 and the cluster T2 are marked in green and blue, respectively. Bidirected arcs are highlighted with blue for clarity.