Data fusion--the process of combining observational and exp erimental data--can enable the identification of causal effects that would otherwise rem ain non-identifiable. Although identification algorithms have been developed for specific s cenarios, do-calculus remains the only general-purpose tool for causal data fusion, particul arly when variables are present in some data sources but not others. However, approaches based on do-calculus may encounter computational challenges as the number of variables increa ses and the causal graph grows in complexity. Consequently, there exists a need to reduce t he size of such models while preserving the essential features. For this purpose, we pro pose pruning (removing unnecessary variables) and clustering (combining variables) as pr eprocessing operations for causal data fusion. We generalize earlier results on a single data s ource and derive conditions for applying pruning and clustering in the case of multiple data sources. We give sufficient conditions for inferring the identifiability or non-identi fiability of a causal effect in a larger graph based on a smaller graph and show how to obtain the corre sponding identifying functional for identifiable causal effects. Examples from ep idemiology and social science demonstrate the use of the results.

Graphs are commonly used to represent and visualize causal relations. For a small number of variables, this approach provides a succinct and clear view of the scenario at hand. As the number of variables under study increases, the graphical approach may become impractical, and the clarity of the representation is lost. Clustering of variables is a natural way to reduce the size of the causal diagram but it may erroneously change the essential properties of the causal relations if implemented arbitrarily. We define a specific type of cluster, called transit cluster, that is guaranteed to preserve the identifiability properties of causal effects under certain conditions. We provide a sound and complete algorithm for finding all transit clusters in a given graph and demonstrate how clustering can simplify the identification of causal effects. We also study the inverse problem, where one starts with a clustered graph and looks for extended graphs where the identifiability properties of causal effects remain unchanged. We show that this kind of structural robustness is closely related to transit clusters.