On 7/8/19 1:59 PM, Jarrett Byrnes wrote:
> This is awesome. Can you elaborate to the listserv what is Structural
> After Measurement?
It is only relevant if you have a model with multiple (measured) latent
variables, and the focus is on the structural part: the regressions
among those latent variables.
In a nutshell, it is an implementation of an old idea (Burt, 1973, 1976)
that we should first estimate the measurement part(s) of the model, and
only then (keeping the measurement parameters fixed) estimate the
structural part of the model. This is in contrast with the standard
approach, where all parameters are estimated jointly (system-wide).
Unfortunately, there is no paper yet: I am currently writing this up.
However, special cases of the SAM approach are known as 'factor score
regression with Croon's correction'. Below are a few references.
Yves.
Burt, R. S. (1973). Confirmatory factor-analytic structures and the
theory construction process. Sociological Methods & Research, 2(2), 131-190.
Burt, R. S. (1976). Interpretational confounding of unobserved variables
in structural equation models. Sociological methods & research, 5(1), 3-52.
Devlieger, I., Mayer, A., & Rosseel, Y. (2016). Hypothesis testing using
factor score regression: A comparison of four methods. Educational and
psychological measurement, 76(5), 741-770.
Devlieger, I., & Rosseel, Y. (2017). Factor score path analysis.
Methodology, 13, 31-38.
Devlieger, I., Talloen, W., & Rosseel, Y. (2019). New Developments in
Factor Score Regression: Fit Indices and a Model Comparison Test.
Educational and Psychological Measurement, 0013164419844552.
Takane, Y., & Hwang, H. (2018). Comparisons among several consistent
estimators of structural equation models. Behaviormetrika, 45(1), 157-188.