Moderation test fit indices
Message/Author
 Viktoriya Magid posted on Wednesday, June 17, 2009 - 7:45 pm
Dear Dr. Muthen,

I was hoping to get clarity on the moderation results I found.

1) First, I tested the model in one sample to make sure it's fitting well (÷2 = 6556.63, df = 3131, p<.01; CFI = .93; TLI = .93; RMSEA = .04).
2) Second, I tested the 2-sample model (males and females) where I contrained 4 paths of interest between groups (÷2 = 12209.30, df = 6279, p <.01; TLI = .85; CFI = .85; RMSEA = .05).
3) Third, I uncontrained these 4 paths to test for chi square difference (÷2 = 12199.70, df = 6275, p <.01; TLI = .85; CFI = .85; RMSEA = .05).

Given that I did not explicitly code for any other contraints, I'm struggling to understand why the model fit of the third model is not approximating that of the first model (single sample) if there are no between-group constraints in the third model. Does Mplus automatically place constraints on any parameters (e.g., variances, errors)?

Thank you in advance for your help,
Viktoriya Magid
 Linda K. Muthen posted on Thursday, June 18, 2009 - 8:53 am
In 3, it looks like some parameters are still constrained. If they were all unconstrained, the degrees of freedom would be 6262. They are not. See TECH1 to find the parameters that are still constrained to be equal.
 Chang Liu posted on Friday, July 21, 2017 - 8:57 am
Dear Dr. Muthen,

I hope you are doing well! I have a quick question about the moderation analysis with covariates. I am working on the moderation analysis (e.g., examining the influence of A, B and A*B on Y) while controlling for the influence of the covariates C and D on Y. The fitting index were good. However, when I correlated the covariance of A and C, the fitting index TLI turned to negative and CFI turned to 0. Do you think the change of the fitting index is an issue of statistical model that I do not need to worry about?

Many thanks!
 Bengt O. Muthen posted on Friday, July 21, 2017 - 2:14 pm
I don't see why the model isn't saturated (just-identified; has zero df). Send the 2 outputs you refer to to Support along with your license number.
 Chang Liu posted on Saturday, July 22, 2017 - 11:21 am
Thank you for your quick reply! In the model, I also asked for the covariance of A and D, and the covariance of C and D. I guess that's why the model is not saturated.