A Note on Exploratory Item Factor Analysis by Singular Value Decomposition
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In this note, we revisit a singular value decomposition (SVD) based algorithm that was given in Chen et al. (2019a) for obtaining an initial value for joint maximum likelihood estimation of exploratory Item Factor Analysis (IFA). This algorithm estimates a multidimensional item response theory model by SVD. Thanks to the computational efficiency and scalability of SVD, this algorithm has substantial computational advantage over other exploratory IFA algorithms, especially when the numbers of respondents, items, and latent dimensions are all large. Under the same double asymptotic setting and notion of consistency as in Chen et al. (2019a), we show that this simple algorithm provides a consistent estimator for the loading matrix up to a rotation. This result provides theoretical guarantee to the use of this simple algorithm for exploratory IFA.
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