  We revisit a singular value decomposition (SVD) algorithm given in Chen et
al. (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 (PCA) 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.
