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Spanning trees and identifiability of a single-factor model

Author

Listed:
  • Claudia Tarantola

    (Università di Pavia)

  • Paola Vicard

    (Università Roma Tre)

Abstract

The aim of this paper is to propose conditions for exploring the class of identifiable Gaussian models with one latent variable. In particular, we focus attention on the topological structure of the complementary graph of the residuals. These conditions are mainly based on the presence of odd cycles and bridge edges in the complementary graph. We propose to use the spanning tree representation of the graph and the associated matrix of fundamental cycles. In this way it is possible to obtain an algorithm able to establish in advance whether modifying the graph corresponding to an identifiable model, the resulting graph still denotes identifiability.

Suggested Citation

  • Claudia Tarantola & Paola Vicard, 2002. "Spanning trees and identifiability of a single-factor model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 11(2), pages 139-152, June.
    • Handle: RePEc:spr:stmapp:v:11:y:2002:i:2:d:10.1007_bf02511482
    DOI: 10.1007/BF02511482
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    References listed on IDEAS

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    1. N/A, 1995. "Statistical Appendix," National Institute Economic Review, National Institute of Economic and Social Research, vol. 151(1), pages 95-104, February.
    2. Paolo Giudici & Elena Stanghellini, 2001. "Bayesian inference for graphical factor analysis models," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 577-591, December.
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