On Extended Guttman Condition in High Dimensional Factor Analysis

Kentaro Hayashi, Ke Hai Yuan, Ge (Gabriella) Jiang

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.

Original languageEnglish (US)
Title of host publicationQuantitative Psychology - 83rd Annual Meeting of the Psychometric Society, 2018
EditorsRianne Janssen, Dylan Molenaar, Marie Wiberg, Jorge González, Steven Culpepper
Number of pages8
ISBN (Print)9783030013097
StatePublished - 2019
Event83rd Annual meeting of the Psychometric Society, 2018 - New York, United States
Duration: Jul 9 2018Jul 13 2018

Publication series

NameSpringer Proceedings in Mathematics and Statistics
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017


Conference83rd Annual meeting of the Psychometric Society, 2018
Country/TerritoryUnited States
CityNew York


  • High dimensions
  • Principal components
  • Unique variances

ASJC Scopus subject areas

  • Mathematics(all)


Dive into the research topics of 'On Extended Guttman Condition in High Dimensional Factor Analysis'. Together they form a unique fingerprint.

Cite this