Compatibility of ID.cat = "Wu.Estabrook.2016" with measEq.syntax and Multiple-Group SEM

[ahmad valikhani]

Hi,

I’m running a multiple-group SEM with both categorical and continuous indicators. Prior to this, I established measurement invariance across groups using measEq.syntax. For identification, I used:

parameterization = "theta",
estimator = "WLSMV",
ID.fac = "std.lv",
ID.cat = "Wu.Estabrook.2016",
group = "sex"

This approach is highly recommended for testing measurement invariance of categorical indicators.

After establishing measurement invariance, I now want to compare regression coefficients (structural paths) across groups, not latent means. Since “standardizing common factors by fixing their variances to 1.0 is incorrect if groups differ in their variabilities” (Kline, 2023), I’m concerned that using std.lv (which standardizes latent variances in each group) may obscure true differences in factor variances and make path comparisons less meaningful.

My question is: What is the recommended here to do? Shoudl I maintain this method while transitioning to multiple-group SEM for structural paths? Or is it more appropriate to switch to fixing the loading for the reference indicator to 1.0 (i.e., leave the factor unstandardized) in multiple-group SEM?

Thank you very much for your help in advance.

Best,

A