Structural comparison in multi-group SEM PreviousNext
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 Josie Booth posted on Wednesday, July 07, 2010 - 3:57 am

I'm carrying out mulit-group SEM and looking for a bit of advice please. I have metric and scalar invariance and have compared the latent means of the two groups. In addition to this I would like to assess whether the regression weights for the structural paths are the same or not. I get a significant delta chi-square when I compare the model with the paths constrained to be equal to one where they are free. I have then freed each path individually while constraining the others to be equal. I get a significant delta chi-square every time but when I look at the regression weights for each group they are overlapping (using 1.96xSE) thus suggesting that they don't actually differ. I'm aware that the significant change to the chi-square could be due to the totality of the changes made by freeing just one parameter but I'm unsure as to the conclusions which can be drawn.

Firstly, is my logic correct and if so can I conclude that the paths are the same between groups? Secondly, is there a more appropriate way of assessing this?

In addition when all paths are free, I get extremely large standard errors for one group (Est 10.57, SE 14.36 & Est 12.71, SE 15.28). Should I be concerned about the size of these SE's? When looking at the standardised solution these SE's are greater than one - is this acceptable?

Thank you for any help which you can provide.

 Bengt O. Muthen posted on Wednesday, July 07, 2010 - 9:54 am
You can instead make a path equal across the groups while letting the other paths be different across groups.

If SEs for one group are much larger without its sample size being much smaller, I would do a separate analysis of this group to see if the SEs are large then also.
 Josie Booth posted on Thursday, July 08, 2010 - 7:25 am
Thank you very much for your help.

I have done a separate analysis for each group and the standard errors are much more appropriate. I wonder if you could possibly advise as to why it makes such a difference to the standard errors estimating the two groups in the same or different analysis?


 Linda K. Muthen posted on Friday, July 09, 2010 - 10:12 am
The equality across groups may be causing this. If you have further questions, please send the outputs in question and your license number to
 Brianna H posted on Thursday, March 20, 2014 - 8:37 am
Hello. I am transitioning from conducting multi-group SEM in AMOS to Mplus. In Mplus, I would like to know whether a model where the structural weights of the two groups are constrained to be equal fits no worse than the saturated model where they are estimated uniquely. (In AMOS, this is determined via nested model comparisons assuming the unconstrained model to be correct, e.g. structural weights, intercepts, and means.)

In the Mplus output for a multi-group model, I see only the usual model fit information such as the Model Chi-sq, CFI, RMSEA, etc. Does Mplus provide nested model comparison statistics for a multi-group model? The output I requested is "MODINDICES (ALL) STAND SAMPSTAT TECH4." Thank you for your help.
 Linda K. Muthen posted on Thursday, March 20, 2014 - 1:37 pm
Mplus does automatic difference testing only for measurement invariance. For your model you would need to do the difference test after running the two analyses.
 Brianna H posted on Thursday, March 20, 2014 - 9:38 pm
Thank you-- since there are no latent variables in my multi-group SEM model, I'm assuming that the measurement invariance test is not applicable to my model?

Can you clarify what is the difference test and what syntax would allow me to run it? Or is the difference test just a chi-square difference test for the two models, subtracting the chi-square values and df's from each other? Thanks again for your reply.
 Linda K. Muthen posted on Friday, March 21, 2014 - 7:01 am
You are correct. Invariance testing involves latent variables.

For ML, it is as you state. Difference tests for MLR are described on the website. See the left column. With WLSMV and MLMV, use the DIFFTEST option. See Example 13.12
 Brianna H posted on Friday, March 21, 2014 - 9:45 am
Thank you.
 Rachel posted on Saturday, March 21, 2015 - 3:40 pm

I am doing a multi-group SEM and am trying to figure out which pathways are contributing to model non invariance. after releasing each constraint one at a time, the model fit barely improved.

The mod indices suggest adding a path which doesn't theoretically make sense since it suggests I regress my mediator on my independent variable.

I am trying to write these results. Do I interpret this as all the paths varying across groups? Or is there something I am missing?

 Bengt O. Muthen posted on Monday, March 23, 2015 - 2:41 pm
Don't know if this is a multiple-indicator model in which case the question is how well the configural model fits, or if it is path analysis with all observed variables but some kind of over-identification in each group in which case the question is what the fit in each group separately is.
 Margarita  posted on Monday, September 19, 2016 - 3:11 am
Dear Dr. Muthen,

After confirming PARTIAL measurement invariance (across time and gender) for 2 latent factors, I want to run a multigroup cross-lag model that uses the 2 latent factors.

I have all cross-lag paths to be freely estimated (H0) vs constrained to be equal across gender (H1) to see whether they are gender-invariant, but I am not sure how to treat the two latent variables. Should I constrain them to be equal across groups (in H0 and H1), leave them vary across groups, or constrain only the factor loadings/thresholds that were found to be invariant (since I found partial invariance)?

Thank you in advance
 Margarita  posted on Monday, September 19, 2016 - 5:34 am
Apologies for posting again, but I found the answer in a book. I will set the scalar parameters to be equal across gender, except for those that were found to be non-invariant.

Thank you anyway!
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