  We investigate novel parameter estimation and goodness-of-fit (GOF)
assessment methods for large-scale confirmatory item factor analysis (IFA) with
many respondents, items, and latent factors. For parameter estimation, we
extend Urban and Bauer's (2021) deep learning algorithm for exploratory IFA to
the confirmatory setting by showing how to handle constraints on loadings and
factor correlations. For GOF assessment, we explore simulation-based tests and
indices that extend the classifier two-sample test (C2ST), a method that tests
whether a deep neural network can distinguish between observed data and
synthetic data sampled from a fitted IFA model. Proposed extensions include a
test of approximate fit wherein the user specifies what percentage of observed
and synthetic data should be distinguishable as well as a relative fit index
(RFI) that is similar in spirit to the RFIs used in structural equation
modeling. Via simulation studies, we show that: (1) the confirmatory extension
of Urban and Bauer's (2021) algorithm obtains comparable estimates to a
state-of-the-art estimation procedure in less time; (2) C2ST-based GOF tests
control the empirical type I error rate and detect when the latent
dimensionality is misspecified; and (3) the sampling distribution of the
C2ST-based RFI depends on the sample size.
