  Confirmatory factor analysis (CFA) is a statistical method for identifying
and confirming the presence of latent factors among observed variables through
the analysis of their covariance structure. Compared to alternative factor
models, CFA offers interpretable common factors with enhanced specificity and a
more adaptable approach to modeling covariance structures. However, the
application of CFA has been limited by the requirement for prior knowledge
about "non-zero loadings" and by the lack of computational scalability (e.g.,
it can be computationally intractable for hundreds of observed variables). We
propose a data-driven semi-confirmatory factor analysis (SCFA) model that
attempts to alleviate these limitations. SCFA automatically specifies "non-zero
loadings" by learning the network structure of the large covariance matrix of
observed variables, and then offers closed-form estimators for factor loadings,
factor scores, covariances between common factors, and variances between errors
using the likelihood method. Therefore, SCFA is applicable to high-throughput
datasets (e.g., hundreds of thousands of observed variables) without requiring
prior knowledge about "non-zero loadings". Through an extensive simulation
analysis benchmarking against standard packages, SCFA exhibits superior
performance in estimating model parameters with a much reduced computational
time. We illustrate its practical application through factor analysis on a
high-dimensional RNA-seq gene expression dataset.
