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A note on exploratory item factor analysis by singular value decomposition

Zhang, Haoran, Chen, Yunxiao ORCID: 0000-0002-7215-2324 and Li, Xiaoou (2020) A note on exploratory item factor analysis by singular value decomposition. Psychometrika, 85 (2). 358 - 372. ISSN 0033-3123

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Identification Number: 10.1007/s11336-020-09704-7


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.

Item Type: Article
Official URL:
Additional Information: © 2020 The Authors
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 28 Apr 2020 16:36
Last Modified: 11 Jan 2022 15:21

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