On the identification of path analysis models with one hidden variable

We study criteria for identifiability of path analysis models with one hidden variable. We first derive sufficient criteria for identification of models in which marginalisation is carried out over the hidden variable. The sufficient criteria are based on the structure of the directed acyclic graph associated with the path analysis model and can be derived from the graph. We treat further the identification of models when the hidden variable is conditioned on and establish connections with the extended skew-normal distribution. Finally it is shown that the derived conditions extend the existing graphical criteria for identification. Copyright 2005, Oxford University Press.