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 Marlies Maes posted on Monday, September 16, 2013 - 7:38 am
Dear all,

I established measurement invariance for 4 groups, for a model including 4 factors with 3 indicators each.

As a next step, I would like to compare the latent means across those four groups. By default, the first factor mean is constrained to zero.

(a) Is is possible to compare latent means across groups, without constraining any of those latent means to zero?
Or: how can I obtain the latent means for each group? (without one being set to zero)

(b) Is it correct that when I would like to see which groups differ from each other, I need to examine this per pair of groups?

Many thanks for your help.

Best wishes,
Marlies
 Linda K. Muthen posted on Monday, September 16, 2013 - 11:14 am
To compare all factor means, use a model with factor means zero in all groups versus a model with factor means zero in one group and free in the other groups.

To compare specific pairs of means if you have, for example, three groups and the factor means are fixed to zero in the first group, the z-test of the factor mean in group 2 tests the difference between groups 1 and 2. The z-test of the factor mean in group 2 tests he difference between groups 1 and 3. Use MODEL TEST to test the difference between groups 2 and 3.
 Marlies Maes posted on Tuesday, September 17, 2013 - 1:20 am
Many thanks for your quick answer!

Is it also possible to just see the factor means for each group?

(In other words, is it possible to see the latent mean of each factor for each group, without one being set to zero?)

Many thanks for your help!
 Linda K. Muthen posted on Tuesday, September 17, 2013 - 7:11 am
No. One must be set to zero for identification.
 Ebrahim Hamedi posted on Tuesday, November 05, 2013 - 6:22 pm
Hello,
On page 433, you mention three possible steps for measurement invariance testing:

excerpt from the manual:
"1. Intercepts, factor loadings, and residual variances free across groups;
factor means fixed at zero in all groups
2. Factor loadings constrained to be equal across groups; intercepts and
residual variances free; factor means fixed at zero in all groups
3. Intercepts and factors loadings constrained to be equal across
groups; residual variances free; factor means zero in one group and
free in the others (the Mplus default)"


I have a question: Given that, in step 3, latent means in one group are fixed to zero, and freely estimated in other groups, I believe, in addition to providing a test of scalar invariance, estimates of step 3 can be used for investigating differences in latent means across groups. That is, the latent means in other groups can be tested for significance relative to the latent means in the reference group. Do you agree with my understanding? Or do you suggest extra modeling for latent mean analysis following scalar invariance testing?

many thanks in advance,
Ebi
 Bengt O. Muthen posted on Wednesday, November 06, 2013 - 8:36 am
I agree with your understanding.
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