No surprised he brought it up long before we did! It's definitely uncomfortable to look at the models and see that they have different meanings and then write the model equations out to see that they are the same. It seems like there should be a simple fix, but it gets really messy really fast!
Similar idea as the SAM work! ( p. 13 of the journal version talks about relation between the two methods). The difference is the mechanism. I believe the SAM work relies on a correction, our paper tries to use Bayes to model things directly. There are pros and cons of each approach, of course!
Non-paywalled version: www.researchgate.net/publication/...
PDF | Research in education and behavioral sciences often involves the use of latent variable models that are related to indicators, as well as related... | Find, read and cite all the research you ne...
The benefit of the method is that it facilitates embedding measurement models into larger models without having to deal with latent variable scores. /5
The paper describes how to preserve both measurement and uncertainty simultaneously with multistage Bayesian estimation, even if the indicators are categorical /4
Constraining loadings or fitting the model in pieces can preserve measurement but not the uncertainty, so the estimates and their standard errors can be inaccurate (it is not uncertainty preserving). /3
If estimated jointly, the path diagram on the left (that is intended to regress an observed variable on a latent predictor) will include the outcome into the measurement model of the latent variable, unintendedly changing the meaning of the latent variable (it is not measurement preserving). /2
New paper w/ Roy Levy These 2 path diagrams are conceptually different (regression with a latent predictor that has 3 indicators vs. a factor model with 4 indicators) but they are mathematically equivalent. journals.sagepub.com/doi/10.3102/... /1
This is fantastic news, super excited for you!!
Psychology really needs to go back to square 1 on measurement. Even the major replications haven’t taken the lack of valid measures seriously. We are making up questions and questionnaires daily w/o validating constructs or tasks. This means our foundation is seriously shaky @jkflake.bsky.social