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