A Note on Exploratory Item Factor Analysis by Singular Value Decomposition

Haoran Zhang (), Yunxiao Chen () and Xiaoou Li ()
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Haoran Zhang: Fudan University
Yunxiao Chen: London School of Economics and Political Science
Xiaoou Li: University of Minnesota

Psychometrika, 2020, vol. 85, issue 2, No 5, 358-372

Abstract: 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.

Keywords: exploratory item factor analysis; IFA; singular value decomposition; double asymptotics; generalized PCA for binary data (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11336-020-09704-7

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