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A Note on Exploratory Item Factor Analysis by Singular Value Decomposition

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...

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Autores principales: Zhang, Haoran, Chen, Yunxiao, Li, Xiaoou
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7385012/
https://www.ncbi.nlm.nih.gov/pubmed/32451743
http://dx.doi.org/10.1007/s11336-020-09704-7
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author Zhang, Haoran
Chen, Yunxiao
Li, Xiaoou
author_facet Zhang, Haoran
Chen, Yunxiao
Li, Xiaoou
author_sort Zhang, Haoran
collection PubMed
description 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. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (10.1007/s11336-020-09704-7) contains supplementary material, which is available to authorized users.
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spelling pubmed-73850122020-08-11 A Note on Exploratory Item Factor Analysis by Singular Value Decomposition Zhang, Haoran Chen, Yunxiao Li, Xiaoou Psychometrika Theory and Methods 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. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (10.1007/s11336-020-09704-7) contains supplementary material, which is available to authorized users. Springer US 2020-05-26 2020 /pmc/articles/PMC7385012/ /pubmed/32451743 http://dx.doi.org/10.1007/s11336-020-09704-7 Text en © The Author(s) 2020 Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Theory and Methods
Zhang, Haoran
Chen, Yunxiao
Li, Xiaoou
A Note on Exploratory Item Factor Analysis by Singular Value Decomposition
title A Note on Exploratory Item Factor Analysis by Singular Value Decomposition
title_full A Note on Exploratory Item Factor Analysis by Singular Value Decomposition
title_fullStr A Note on Exploratory Item Factor Analysis by Singular Value Decomposition
title_full_unstemmed A Note on Exploratory Item Factor Analysis by Singular Value Decomposition
title_short A Note on Exploratory Item Factor Analysis by Singular Value Decomposition
title_sort note on exploratory item factor analysis by singular value decomposition
topic Theory and Methods
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7385012/
https://www.ncbi.nlm.nih.gov/pubmed/32451743
http://dx.doi.org/10.1007/s11336-020-09704-7
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