Dear all,
I was just working with measurement invariance testing using lavaan and semTools::miPowerFit function and have some doubts about standardized parameters and unstandardized parameters, and how to interpret them. I found resources discussing the issue of how standardized loadings are to be interpreted (e.g., Brown, 2015), but I couldn't find a resource discussing how standardized intercepts are to be interpreted. Thus, my questions are:
1. How are standardized intercepts to be interpreted? How are standardized intercepts transformed back to unstandardized intercepts? Are there any good resources on this?
I think this question is of interest for lavaan users in general who use an standardized solution. However, in the context of invariance testings, it is equality of unstandardized parameters what we are interested in (see this thread for a nice explanation and discussion:
https://groups.google.com/g/lavaan/c/eRRgQwWrkt4/m/r9eK39WNB00J ). But if one engages in measurement invariance testing using miPowerFit, there's the option of introducing sizes of "standardized factor loadings" and "standardized intercepts" that one would like to be detected (i.e., kind of like "effect sizes" that are too big). Therefore:
2. If in measurement invariance testing what we care is about unstandardized loadings and unstandardized intercepts, should we use standardized effect sizes in miPowerFit for MI testing - for instance for detecting partial measurement invariance? Would this mean we are indeed using different unstandardized thresholds for each item and group? Would that make sense?
I hope the question is of interest and somebody is able to answer it.
Best,
Carlos