On Extended Guttman Condition in High Dimensional Factor Analysis

  • Kentaro HayashiEmail author
  • Ke-Hai Yuan
  • Ge (Gabriella) Jiang
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 265)


It is well-known that factor analysis and principal component analysis often yield similar estimated loading matrices. Guttman (Psychometrika 21:273–285, 1956) identified a condition under which the two matrices are close to each other at the population level. We discuss the matrix version of the Guttman condition for closeness between the two methods. It can be considered as an extension of the original Guttman condition in the sense that the matrix version involves not only the diagonal elements but also the off-diagonal elements of the inverse matrices of variance-covariances and unique variances. We also discuss some implications of the extended Guttman condition, including how to obtain approximate estimates of the inverse of covariance matrix under high dimensions.


High dimensions Principal components Unique variances 



The authors are thankful to Dr. Dylan Molenaar’s comments. Ke-Hai Yuan’s work was supported by the National Science Foundation under Grant No. SES-1461355.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Kentaro Hayashi
    • 1
    Email author
  • Ke-Hai Yuan
    • 2
  • Ge (Gabriella) Jiang
    • 3
  1. 1.Department of PsychologyUniversity of Hawaii at ManoaHonoluluUSA
  2. 2.Department of PsychologyUniversity of Notre DameNotre DameUSA
  3. 3.Department of Educational PsychologyUniversity of Illinois at Urbana-ChampaignUrbana-ChampaignUSA

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