Singular value decomposition of probability matrices: Probabilistic aspects of latent dichotomous variables

Zvi Gilula*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

This paper gives a matrix approach to determine when a statistical dependence between two manifest categorical random variables can be viewed as generated by some unobserved latent variables, in the sense that the manifest variables are conditionally independent with respect to the latent variables. By the singular value decomposition of the matrix representing deviations from statistical independence of the two manifest variables, we give a necessary and sufficient condition for existence of dichotomous latent variables, which are 'responsible' for conditional independence. We give a technique for identifying the distributions of such latent variables and also the conditional distributions of the manifest variables given the latent variables. Finally, we discuss some probabilistic aspects.

Original languageEnglish
Pages (from-to)339-344
Number of pages6
JournalBiometrika
Volume66
Issue number2
DOIs
StatePublished - Aug 1979
Externally publishedYes

Keywords

  • Identifiability
  • Latent variable
  • Manifest variable
  • Singular value decomposition

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