Convergence of estimates of unique variances in factor analysis, based on the inverse sample covariance matrix

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Abstract

If the ratio m/p tends to zero, where m is the number of factors m and p the number of observable variables, then the inverse diagonal element of the inverted observable covariance matrix (σ pjj) -1 tends to the corresponding unique variance ψ jj for almost all of these (Guttman, 1956). If the smallest singular value of the loadings matrix from Common Factor Analysis tends to infinity as p increases, then m/p tends to zero. The same condition is necessary and sufficient for (σ pjj) -1 to tend to ψ jj for all of these. Several related conditions are discussed. © 2006 The Psychometric Society.
Original languageEnglish
Pages (from-to)193-199
JournalPsychometrika. Vol 67(1)
Volume71
Issue number1
DOIs
Publication statusPublished - 1 Mar 2006

Keywords

  • common factor analysis
  • confirmatory factor analysis
  • image factor analysis

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