I have questions about whether a colleague's statistical approach is appropriate. They are looking at whether the effects of 9 continuous predictors on a continuous outcome differ between 3 natural / non-assigned groups. All variables are directly measured - no latent variables. They do this by examining multiple group models in Mplus as follows:
- Estimate a model in which the outcome is regressed on all 9 predictors, separately in group A and group B, but with all regression paths constrained to be equal between groups A and B. (Intercepts and variances not constrained.)
- Estimate the same model, but with the regression path for predictor 1 only freed to vary between groups.
- If chi-square difference between the two models is significant, conclude that the paths significantly differ.
Repeat steps 2 and 3 for predictors 2 - 9.
Repeat steps 1 through 4, but this time in groups A and C.
My basic question is whether this seems like an appropriate approach. More specifically:
- Is there a good paper or reference describing this method so I can understand it better? I have a very basic understanding of SEM (took a course a few years ago but never really used it) and understand the logic of their approach, but I don't have a strong enough understanding to know if they're really using it appropriately.
- Would outcomes from this approach differ radically from results of moderated regression? i.e., using dummy codes for group, computing interaction terms, and using simple slopes to follow up interactions? I feel like moderated regression would be a lot "cleaner," but I may be biased by familiarity. Is there any reason to prefer either their multiple groups modeling approach or more standard moderated regression?
- Is a significant chi-square difference test sufficient to conclude there's a meaningful difference between paths? Is it overly sensitive to sample size? Their groups are approx 150 to 225 people each.
- Do they need to demonstrate measurement invariance before testing differences between individual paths? I believe this is necessary when testing paths among latent variables (?), but maybe not if only manifest variables are included?