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On Extended Guttman Condition in High Dimensional Factor Analysis

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Quantitative Psychology (IMPS 2017, IMPS 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 265))

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.

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Acknowledgements

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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Authors and Affiliations

  1. Department of Psychology, University of Hawaii at Manoa, 2530 Dole Street, Sakamaki C400, Honolulu, HI, 96822, USA

    Kentaro Hayashi

  2. Department of Psychology, University of Notre Dame, Corbett Family Hall, Notre Dame, IN, 46556, USA

    Ke-Hai Yuan

  3. Department of Educational Psychology, University of Illinois at Urbana-Champaign, 1310 South 6th Street, Campaign, Urbana-Champaign, IL, 61820, USA

    Ge (Gabriella) Jiang

Authors
  1. Kentaro Hayashi
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  2. Ke-Hai Yuan
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  3. Ge (Gabriella) Jiang
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Corresponding author

Correspondence to Kentaro Hayashi .

Editor information

Editors and Affiliations

  1. Department of Statistics, Umeå School of Business, Economics and Statistics, Umeå University, Umeå, Sweden

    Marie Wiberg

  2. Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, IL, USA

    Steven Culpepper

  3. Faculty of Psychology and Educational Sciences, KU Leuven, Leuven, Belgium

    Rianne Janssen

  4. Facultad de Matematicas, Pontificia Universidad Catolica de Chile, Santiago, Chile

    Jorge González

  5. Department of Psychology, University of Amsterdam, Amsterdam, The Netherlands

    Dylan Molenaar

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Hayashi, K., Yuan, KH., Jiang, G.(. (2019). On Extended Guttman Condition in High Dimensional Factor Analysis. In: Wiberg, M., Culpepper, S., Janssen, R., González, J., Molenaar, D. (eds) Quantitative Psychology. IMPS IMPS 2017 2018. Springer Proceedings in Mathematics & Statistics, vol 265. Springer, Cham. https://doi.org/10.1007/978-3-030-01310-3_20

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