A Note on Exploratory Item Factor Analysis by Singular Value Decomposition

Haoran Zhang, Yunxiao Chen, Xiaoou Li

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We revisit a singular value decomposition (SVD) algorithm given in Chen et al. (Psychometrika 84:124–146, 2019b) for exploratory item factor analysis (IFA). This algorithm estimates a multidimensional IFA model by SVD and was used to obtain a starting point for joint maximum likelihood estimation in Chen et al. (2019b). Thanks to the analytic and computational properties of SVD, this algorithm guarantees a unique solution and has computational advantage over other exploratory IFA methods. Its computational advantage becomes significant when the numbers of respondents, items, and factors are all large. This algorithm can be viewed as a generalization of principal component analysis to binary data. In this note, we provide the statistical underpinning of the algorithm. In particular, we show its statistical consistency under the same double asymptotic setting as in Chen et al. (2019b). We also demonstrate how this algorithm provides a scree plot for investigating the number of factors and provide its asymptotic theory. Further extensions of the algorithm are discussed. Finally, simulation studies suggest that the algorithm has good finite sample performance.

Original languageEnglish (US)
Pages (from-to)358-372
Number of pages15
JournalPsychometrika
Volume85
Issue number2
DOIs
StatePublished - Jun 1 2020

Bibliographical note

Funding Information:
Yunxiao Chen acknowledges the support from the National Academy of Education/Spencer Postdoctoral Fellowship. Xiaoou Li acknowledges the support from NSF under the grant DMS-1712657.

Funding Information:
Yunxiao Chen acknowledges the support from the National Academy of Education/Spencer Postdoctoral Fellowship. Xiaoou Li acknowledges the support from NSF under the grant DMS-1712657.

Publisher Copyright:
© 2020, The Author(s).

Keywords

  • IFA
  • double asymptotics
  • exploratory item factor analysis
  • generalized PCA for binary data
  • singular value decomposition

PubMed: MeSH publication types

  • Journal Article
  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.

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