I have a two models that I would like to compare for model fit but having issues with obtaining equal fit statistics across both models.
Model 1: Mediation model (X, M and Y) with latent factors, using WLSMV estimator because of categorical indicators for X and M.
Model 2: Mediated/moderation, same as above with an observed moderator. Mplus allocates an MLR estimator.
I'm having issues with comparing models because Model 1 does not give AIC/BIC values and Model 2 only gives AIC/BIC values.
Question: Is there anyway to request fit statistics for either of these models that will allow me to compare fit? I did contemplate running Model 1 using MLR estimator, but I have done all my CFA's using WLSMV and find the fit is much better than MLR.
You can use WLSMV with an observed moderator, for instance using 2-group analysis.
Note that MLR can be used not only for continuous indicators but also for categorical indicators. I say that because of your statement that MLR gives worse fit than WLSMV - I suspect you think MLR is synonymous with treating the indicators as continuous.
But with categorical indicators MLR does not give an overall fit index - although it gives fit info via TECH10. With MLR you can use the loglikelihoods for a chi-square difference test.
Hi Bengt, thank you for your quick response it is much appreciated.
Following on from your answers I have a few more questions (I hope that is okay).
"You can use WLSMV with an observed moderator, for instance using 2-group analysis."
Q: That's very helpful to know, I have some other analyses whereby the moderator is latent so I would like to find a solution whereby I can test the addition of a moderator (i.e. mediation model vs mediated moderation model).
"Note that MLR can be used not only for continuous indicators but also for categorical indicators."
Q: I have run the same mediation model with MLR estimator (using categorical indicators) but I get very different estimation value (i.e. for the indirect effect it is 0.30 for WLSMV and 0.11 for MLR).
"But with categorical indicators MLR does not give an overall fit index - although it gives fit info via TECH10."
Q: I got the message that TECH10 is not available for models with covariates.
"I don't know the nature of your Y so can't tell. Note that MLR defaults to logit link and WLSMV to probit"
My Y is latent (as are my X and M) so if I've understood correctly latent factors are treated as continuous so any relationships between them are linear regressions. Therefore I'm confused as to why the indirect effect would be 0.30 for WLSMV estimator and 0.11 for MLR estimator. Unless I have misunderstood?