I believe Yves Rosseel discusses it briefly in slides 91-93 of his 2014 workshop:
Taken from Rosseel (2014, link above):
Full information approach: marginal maximum likelihood
origins: IRT models (eg Bock & Lieberman, 1970) and GLMMs
the connection with IRT
• the theoretical relationship between SEM and IRT has been well documented:
Takane, Y., & De Leeuw, J. (1987). On the relationship between item
response theory and factor analysis of discretized variables. Psychome-
trika, 52, 393-408.
Kamata, A., & Bauer, D. J. (2008). A note on the relation between factor
analytic and item response theory models. Structural Equation Model-
ing, 15, 136-153.
Joreskog, K. G., & Moustaki, I. (2001). Factor analy-
sis of ordinal variables: A comparison of three approaches. Multivariate
Behavioral Research, 36, 347-387.
when are they equivalent?
• probit (normal-ogive) versus logit: both metrics are used in practice
• a single-factor CFA on binary items is equivalent to a 2-parameter IRT model (Birnbaum, 1968):
In CFA: ... In IRT: ... (see slide)
• a single-factor CFA on polychotomous (ordinal) items is equivalent to the graded response model (Samejima, 1969)
• there is no CFA equivalent for the 3-parameter model (with a guessing parameter)
• the Rasch model is equivalent to a single-factor CFA on binary items, but where all factor loadings are constrained to be equal (and the probit metric is converted to a logit metric)