CFA testing equality of factor means ...
Message/Author
 Calvin D. Croy posted on Friday, August 18, 2006 - 5:13 pm
I have run a multigroup CFA with type = missing H1 with estimator = ML. I have two factors in each of 8 groups. The output provides the factor means in each group, along with the 95% and 99% confidence intervals around the means.
I want to test whether the factor1 means are significantly different across the groups by comparing whether the confidence intervals overlap. In my first group the means of both factors are set at 0.
IS IT VALID FOR ME TO TEST WHETHER FACTOR1's MEAN IN GROUP #2 IS DIFFERENT FROM ITS MEAN IN GROUP #1 BY SEEING WHETHER THE CONFIDENCE INTERVAL IN GROUP 2 INCLUDES 0? I realize that testing for differnces between means by comparing confidence intervals is a conservative approach compared to a t-test etc.
When I test for significant differences between the means of the other groups, I am seeing whether a pair of confidence intervals overlap, but the upper and lower confidence boudaries are all 0 for the group 1 means, which are also 0. I'm a little nervous about not having real confidence intervals around the factor means in group #1 to compare with the intervals around the means in group #2.

 Bengt O. Muthen posted on Friday, August 18, 2006 - 5:21 pm
To test factor mean equality across groups, you can simply use either MODEL TEST or run a model with all groups' means fixed at zero and take the 2*loglikelihood difference between this model and the original one. That seems easier than working with confidence interval?
 Calvin D. Croy posted on Wednesday, August 23, 2006 - 9:01 am
Thank you for your response. I couldn't find the MODEL TEST statement in the Mplus 3.0 User's Guide (though I actually run analyses using version 4.1).

I'm interested in finding which groups have factor means significantly different from those in the first group. Your approaches seem geared to testing whether any means are significantly different from 0, but not necessarily pointing to which ones.

I must be missing something because the approaches you suggest seem like extra work to me since I already have the confidence intervals in my Mplus output.

In a 1-7-05 email from you to me you confirmed that I could test for a significant difference between the means in other groups and the first group's mean of 0 by converting the means in the other groups into Z scores by dividing them by their standard errors and seeing whether any were bigger than 1.96 for a test at the .05 level. This approach seems equivalent to just seeing whether the confidence intervals for the means in the Mplus listing contain 0 -- the method I asked about in my post. Anything wrong with doing this?

Thanks again so much for your help.
-Calvin
 Bengt O. Muthen posted on Wednesday, August 23, 2006 - 7:09 pm
The confidence interval approach works fine if one group has a free factor mean and the other group is the reference group with factor mean fixed at zero. But when you have several groups with free factor means you don't want to use that approach because it is acting as if those free parameter estimates are uncorrelated and they are not (see Tech3). So the 2*logL diff test is useful.