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

[Phil Wood]

My advice would be to check the code to see how the multi-group model is identified. I would think you have latent mean of 0 in one gorup and a freely estimated mean in the other. If that's the case, your standardized regression weights are relative to the second (or more) groups assuming the loadings are the same across groups I would think you're then comparing the unstandardized regression weights across models. Others may want to chime in. Phil