Measurement Invariance: model vs. equ... PreviousNext
Mplus Discussion > Confirmatory Factor Analysis >
 Beth Livingston posted on Wednesday, March 04, 2015 - 9:57 am
I am working through a relatively complex test of measurement invariance. I was hoping to use the "model is configural metric scalar" command to ease this process, by using:

grouping=CONDITION(1=intervention 2=control);

Then the model command in the analysis section.

However, I also have time-based invariance to test along with this grouping variable invariance, so I had essentially set up a model:

T1W by f1
f2-f5 (1-4);

T2W by f1_2
f2_2-f5_2 (1-4);

(and so on...where the constraints indicate equality of loadings by time period)

However, when I, for instance, constrained factor loadings by time (using parentheticals) and intercepts by time (using: [f1 f1_2] (5); etc.), I do not always see those constraints emerge in the "configural" and "metric" models when ostensibly are testing based on group differences, not based on my syntax. When using the "model is configural metric scalar" command, are these additional equality constraints relaxed or ignored? Or is there something I'm missing?

 Bengt O. Muthen posted on Wednesday, March 04, 2015 - 4:17 pm

Model = configural metric scalar;

will ignore any parameter equality settings.

We don't yet have that kind of convenience feature for longitudinal or combined multi-group/long'l, so all of it has to be done "by hand" with explicit equalities.
 Dan Costa posted on Tuesday, June 14, 2016 - 4:21 pm
Dear Drs Muthen,

Iím having trouble finding any documentation about how to examine invariance using the automated method (i.e., model = configural metric scalar). (I prefer to use this method over the alignment method because my data are ordinal.) When Iíve run MGCFA ďmanuallyĒ in the past Iíve used modification indices to determine which parameters to free. As these donít seem to be available for the automated method, what is the recommended method for determining which constraints to relax? Would this be based on examining the largest between-group discrepancies in the unstandardised estimates in the unconstrained model?

 Linda K. Muthen posted on Tuesday, June 14, 2016 - 4:33 pm
Once you have determined that there is noninvariance that you want to understand, you can run the relevant model separately and look at modification indices.
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