MLR model test for invariance in mult... PreviousNext
Mplus Discussion > Multilevel Data/Complex Sample >
 Andy Luse posted on Saturday, August 20, 2016 - 1:14 pm
I'm running a multilevel model where individuals are nested within teams and the teams can consist of all males, all females, or mixed. Based on your paper on Catholic schools, I am testing metric invariance by constricting the loadings across the three group types at the between level. When I compare the output to the configurational invariance model, the Chi square value in the metric model is substantially less and the other fit values also much better (RMSEA, CFI, SRMR). Using the Satorra and Bentler method for Chi square testing of MLR from your site I computed the modified Chi2 (TRd) value and compared this to the critical Chi2 for the change in degrees of freedom between the two models and things seem to line up, but logically it seems strange that the fit measures would get better in a more restrictive model?
 Bengt O. Muthen posted on Saturday, August 20, 2016 - 6:18 pm
We need to see your two outputs - and preferably the data - send to Support along with your license number.
 Andy Luse posted on Sunday, August 21, 2016 - 8:34 pm
Can I ask whether or not it is possible for the Chi2 to be less with the model with more df using MLR?
 Bengt O. Muthen posted on Monday, August 22, 2016 - 1:02 pm
Not if the two models have the same DVs and are set up correctly.
 Andy Luse posted on Tuesday, August 23, 2016 - 5:38 pm
I have been looking all over for example syntax for a multilevel multigroup configurational model syntax and factor loading model syntax and can't seem to find any. Is there some online that I am missing?
 Bengt O. Muthen posted on Wednesday, August 24, 2016 - 10:26 am
I don't think we have exactly that but our short course Topic 7, slides 131 and onward is close. This holds the between loadings group-invariant; so metric invariance. It draws on our paper on our website:

Muthén, B., Khoo, S.T. & Gustafsson, J.E. (1997). Multilevel latent variable modeling in multiple populations. Unpublished technical report.
download paper contact first author show abstract

It would be straight-forward to make the between loading matrices configural instead of metric by just mentioning the between loadings in all groups so they are different.
 Andy Luse posted on Wednesday, August 24, 2016 - 11:15 am
I assume slide 134? Wouldn't you need another model statement for the second group and then in both model statements restrict the loadings at the between level to be equal?

generalb BY y1*(l1);
generalb BY y2(l2);
mathb BY y6*(l16);
mathb BY y8(l17);
 Bengt O. Muthen posted on Wednesday, August 24, 2016 - 5:37 pm
Yes, unless that is the default.
 Andy Luse posted on Thursday, August 25, 2016 - 2:49 pm
Would you still set the residual variances of the items at the between level to zero even though you are restricting the loadings across groups to be equal?
 Bengt O. Muthen posted on Thursday, August 25, 2016 - 4:11 pm
I can go either way with that but perhaps not.
Back to top
Add Your Message Here
Username: Posting Information:
This is a private posting area. Only registered users and moderators may post messages here.
Options: Enable HTML code in message
Automatically activate URLs in message