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On the identification of path analysis models with one hidden variable

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  • Elena Stanghellini
  • Nanny Wermuth

Abstract

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.

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  • Elena Stanghellini & Nanny Wermuth, 2005. "On the identification of path analysis models with one hidden variable," Biometrika, Biometrika Trust, vol. 92(2), pages 337-350, June.
    • Handle: RePEc:oup:biomet:v:92:y:2005:i:2:p:337-350
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    File URL: http://hdl.handle.net/10.1093/biomet/92.2.337
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    Cited by:

    1. Elena Stanghellini & Eduwin Pakpahan, 2015. "Identification of causal effects in linear models: beyond instrumental variables," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 489-509, September.
    2. Manabu Kuroki, 2016. "The Identification of Direct and Indirect Effects in Studies with an Unmeasured Intermediate Variable," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 228-245, March.
    3. Burkhard Raunig, 2019. "Background Indicators," Econometrics, MDPI, vol. 7(2), pages 1-14, May.
    4. Nanny Wermuth & Kayvan Sadeghi, 2012. "Sequences of regressions and their independences," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 215-252, June.
    5. Giovanni Porzio & Maria Vitale, 2007. "Exploring Nonlinearities in Path Models," Quality & Quantity: International Journal of Methodology, Springer, vol. 41(6), pages 937-954, December.

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