On Extended Guttman Condition in High Dimensional Factor Analysis

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

doi:10.1007/978-3-030-01310-3_20

On Extended Guttman Condition in High Dimensional Factor Analysis

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

Educational Psychology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

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 language	English (US)
Title of host publication	Quantitative Psychology - 83rd Annual Meeting of the Psychometric Society, 2018
Editors	Rianne Janssen, Dylan Molenaar, Marie Wiberg, Jorge González, Steven Culpepper
Publisher	Springer
Pages	221-228
Number of pages	8
ISBN (Print)	9783030013097
DOIs	https://doi.org/10.1007/978-3-030-01310-3_20
State	Published - 2019
Event	83rd Annual meeting of the Psychometric Society, 2018 - New York, United States Duration: Jul 9 2018 → Jul 13 2018

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	265
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	83rd Annual meeting of the Psychometric Society, 2018
Country/Territory	United States
City	New York
Period	7/9/18 → 7/13/18

Keywords

High dimensions
Principal components
Unique variances

ASJC Scopus subject areas

General Mathematics

Online availability

10.1007/978-3-030-01310-3_20

Library availability

Discover UIUC Full Text

Cite this

Hayashi, K., Yuan, K. H., & Jiang, G. (2019). On Extended Guttman Condition in High Dimensional Factor Analysis. In R. Janssen, D. Molenaar, M. Wiberg, J. González, & S. Culpepper (Eds.), Quantitative Psychology - 83rd Annual Meeting of the Psychometric Society, 2018 (pp. 221-228). (Springer Proceedings in Mathematics and Statistics; Vol. 265). Springer. https://doi.org/10.1007/978-3-030-01310-3_20

On Extended Guttman Condition in High Dimensional Factor Analysis. / Hayashi, Kentaro; Yuan, Ke Hai; Jiang, Ge (Gabriella).
Quantitative Psychology - 83rd Annual Meeting of the Psychometric Society, 2018. ed. / Rianne Janssen; Dylan Molenaar; Marie Wiberg; Jorge González; Steven Culpepper. Springer, 2019. p. 221-228 (Springer Proceedings in Mathematics and Statistics; Vol. 265).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Hayashi, K, Yuan, KH & Jiang, G 2019, On Extended Guttman Condition in High Dimensional Factor Analysis. in R Janssen, D Molenaar, M Wiberg, J González & S Culpepper (eds), Quantitative Psychology - 83rd Annual Meeting of the Psychometric Society, 2018. Springer Proceedings in Mathematics and Statistics, vol. 265, Springer, pp. 221-228, 83rd Annual meeting of the Psychometric Society, 2018, New York, United States, 7/9/18. https://doi.org/10.1007/978-3-030-01310-3_20

Hayashi, Kentaro ; Yuan, Ke Hai ; Jiang, Ge (Gabriella). / On Extended Guttman Condition in High Dimensional Factor Analysis. Quantitative Psychology - 83rd Annual Meeting of the Psychometric Society, 2018. editor / Rianne Janssen ; Dylan Molenaar ; Marie Wiberg ; Jorge González ; Steven Culpepper. Springer, 2019. pp. 221-228 (Springer Proceedings in Mathematics and Statistics).

@inproceedings{cbef93c70a0640378b572aa85a749059,

title = "On Extended Guttman Condition in High Dimensional Factor Analysis",

abstract = "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.",

keywords = "High dimensions, Principal components, Unique variances",

author = "Kentaro Hayashi and Yuan, {Ke Hai} and Jiang, {Ge (Gabriella)}",

note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.; 83rd Annual meeting of the Psychometric Society, 2018 ; Conference date: 09-07-2018 Through 13-07-2018",

year = "2019",

doi = "10.1007/978-3-030-01310-3_20",

language = "English (US)",

isbn = "9783030013097",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer",

pages = "221--228",

editor = "Rianne Janssen and Dylan Molenaar and Marie Wiberg and Jorge Gonz{\'a}lez and Steven Culpepper",

booktitle = "Quantitative Psychology - 83rd Annual Meeting of the Psychometric Society, 2018",

address = "Germany",

}

TY - GEN

T1 - On Extended Guttman Condition in High Dimensional Factor Analysis

AU - Hayashi, Kentaro

AU - Yuan, Ke Hai

AU - Jiang, Ge (Gabriella)

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - High dimensions

KW - Principal components

KW - Unique variances

UR - http://www.scopus.com/inward/record.url?scp=85066088048&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066088048&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-01310-3_20

DO - 10.1007/978-3-030-01310-3_20

M3 - Conference contribution

AN - SCOPUS:85066088048

SN - 9783030013097

T3 - Springer Proceedings in Mathematics and Statistics

SP - 221

EP - 228

BT - Quantitative Psychology - 83rd Annual Meeting of the Psychometric Society, 2018

A2 - Janssen, Rianne

A2 - Molenaar, Dylan

A2 - Wiberg, Marie

A2 - González, Jorge

A2 - Culpepper, Steven

PB - Springer

T2 - 83rd Annual meeting of the Psychometric Society, 2018

Y2 - 9 July 2018 through 13 July 2018

ER -

On Extended Guttman Condition in High Dimensional Factor Analysis

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Quantitative Psychology: 83rd Annual Meeting of the Psychometric Society, New York, NY 2018

Cite this