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

Research output: Contribution to journalArticleAcademicpeer-review

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 (ςpjj)-1 tends to the corresponding unique variance ψjj 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 (ςpjj)-1 to tend to ψjj for all of these. Several related conditions are discussed. (PsycINFO Database Record (c) 2009 APA, all rights reserved) (journal abstract)
Original languageEnglish
Pages (from-to)193-199
JournalPsychometrika. Vol 67(1)
Volume71
Issue number1
DOIs
Publication statusPublished - Mar 2006

Keywords

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

Cite this

@article{d4d6a203fafd4267b87df74699647cb7,
title = "Convergence of estimates of unique variances in factor analysis, based on the inverse sample covariance matrix",
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 (ςpjj)-1 tends to the corresponding unique variance ψjj 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 (ςpjj)-1 to tend to ψjj for all of these. Several related conditions are discussed. (PsycINFO Database Record (c) 2009 APA, all rights reserved) (journal abstract)",
keywords = "common factor analysis, confirmatory factor analysis, image factor analysis, factoranalyse",
author = "Krijnen, {Wim P.}",
year = "2006",
month = "3",
doi = "10.1007/s11336-000-1142-9",
language = "English",
volume = "71",
pages = "193--199",
journal = "Psychometrika. Vol 67(1)",
issn = "0033-3123",
publisher = "Springer Verlag",
number = "1",

}

Convergence of estimates of unique variances in factor analysis, based on the inverse sample covariance matrix. / Krijnen, Wim P.

In: Psychometrika. Vol 67(1), Vol. 71, No. 1, 03.2006, p. 193-199.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Convergence of estimates of unique variances in factor analysis, based on the inverse sample covariance matrix

AU - Krijnen, Wim P.

PY - 2006/3

Y1 - 2006/3

N2 - 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 (ςpjj)-1 tends to the corresponding unique variance ψjj 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 (ςpjj)-1 to tend to ψjj for all of these. Several related conditions are discussed. (PsycINFO Database Record (c) 2009 APA, all rights reserved) (journal abstract)

AB - 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 (ςpjj)-1 tends to the corresponding unique variance ψjj 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 (ςpjj)-1 to tend to ψjj for all of these. Several related conditions are discussed. (PsycINFO Database Record (c) 2009 APA, all rights reserved) (journal abstract)

KW - common factor analysis

KW - confirmatory factor analysis

KW - image factor analysis

KW - factoranalyse

U2 - 10.1007/s11336-000-1142-9

DO - 10.1007/s11336-000-1142-9

M3 - Article

VL - 71

SP - 193

EP - 199

JO - Psychometrika. Vol 67(1)

JF - Psychometrika. Vol 67(1)

SN - 0033-3123

IS - 1

ER -