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Recursive max-linear vectors provide models for the causal dependence betweenlarge values of observed random variables as they are supported on directedacyclic graphs (DAGs). But the standard assumption that all nodes of such a DAGare observed is often unrealistic. We provide necessary and sufficientconditions that allow for a partially observed vector from a regularly varyingmodel to be represented as a recursive max-linear (sub-)model. Our methodrelies on regular variation and the minimal representation of a recursivemax-linear vector. Here the max-weighted paths of a DAG play an essential role.Results are based on a scaling technique and causal dependence relationsbetween pairs of nodes. In certain cases our method can also detect thepresence of hidden confounders. Under a two-step thresholding procedure, weshow consistency and asymptotic normality of the estimators. Finally, we studyour method by simulation, and apply it to nutrition intake data.

Heavy-tailed max-linear structural equation models in networks with hidden nodes