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Biometrika 2005 92(2):337-350; doi:10.1093/biomet/92.2.337
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© 2005 Biometrika Trust

On the identification of path analysis models with one hidden variable

Elena Stanghellini1 and Nanny Wermuth2

1 Dipartimento di Scienze Statistiche, Universitàdi Perugia, Via A. Pascoli 1, C. P. 1315 Succ.1, 06100 Perugia, Italy elena.stanghellini{at}stat.unipg.it, 2 Department of Mathematical Statistics, Chalmers/Gothenborg University of Technology, S-412 96 Göteborg, Sweden wermuth{at}math.chalmers.se

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.

Key Words: Conditional independence model; Directed acyclic graph; Identification; Latent variable; Linear system; Unobserved confounder

Received December 2002. Revised September 2004.


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