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This paper investigates the impact of variable clustering on causal effect identification in graphical models, demonstrating that arbitrary clustering can distort causal relationships and lead to incorrect inferences. The authors establish conditions for identification invariance, where clustering preserves both identifiability and nonidentifiability of causal effects, by analyzing the c-components of the original causal graph. This work provides a theoretical foundation for simplifying causal graphs while maintaining the integrity of causal effect identification.
Arbitrary variable clustering can invalidate causal effect identification, but a broad class of operations preserving identifiability exists by analyzing c-component structure.
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.