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Statistical Methods and Applications

, Volume 11, Issue 2, pp 139–152 | Cite as

Spanning trees and identifiability of a single-factor model

  • Claudia Tarantola
  • Paola Vicard
Statistical Methods

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.

Key words

Bridge edge graphical Gaussian models identifiability legal moves odd cycle spanning tree 

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Copyright information

© Springer-Verlag 2002

Authors and Affiliations

  • Claudia Tarantola
    • 1
  • Paola Vicard
    • 2
  1. 1.Dipartimento di Economia Politica e Metodi QuantitativiUniversità di PaviaPaviaItaly
  2. 2.Dipartimento di EconomiaUniversità Roma TreRomaItaly

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