Group Means Testing with Covariates
Message/Author
 Ryan Krone posted on Saturday, October 18, 2014 - 9:55 am
Drs. Muthen,

When doing a group comparison using a CFA framework and testing the differences in means between the two groups - the output reports the means.

However, when I regress covariates on the latent factors for the same model the means disappear and now intercepts are reported in the output file.

Are these intercepts still the means? I want to be sure that I'm interpreting them correctly.

Regards,

Ryan
 Linda K. Muthen posted on Saturday, October 18, 2014 - 11:08 am
In a conditional model, intercepts are reported not means. Means are not model parameters in a conditional model.
 Ryan Krone posted on Saturday, October 18, 2014 - 1:05 pm
Right, so these intercepts can be interpreted as the intercepts produced by the regression of the latent factor on the covariates. And the number that the output produces is really the difference between the intercepts across both groups.

Am I on the right track here?
 Linda K. Muthen posted on Saturday, October 18, 2014 - 1:07 pm
Yes.
 Ryan Krone posted on Saturday, October 18, 2014 - 1:30 pm
Thanks Dr. Muthen.
 Henrike Galenkamp posted on Tuesday, March 08, 2016 - 2:58 am
Dear dr. Muthen,

I have tested for measurement invariance of a 12-item scale (2 factors) across three educational groups. The factor loadings, thresholds, residual variances appear to be similar across groups. Now I want to compare the 2 factor means in the strict factorial invariance model (WLSMV, theta parameterization). But only after having added two covariates. From the above I understand that in a conditional model the factor means are not produced, and this is also what I encountered: only intercepts and residual variances are shown for my two factors. Is it possible to obtain the means - adjusted for my covariates - in another way?
 Linda K. Muthen posted on Tuesday, March 08, 2016 - 6:36 am
No. Once they are adjusted for the covariates they are intercepts.
 Henrike Galenkamp posted on Tuesday, March 22, 2016 - 12:38 am
Dear Linda,
Thank you for your reply. Since I want to report mean differences adjusted for my covariates, I have exported the factor scores to SPSS using
FILE IS strict_fs.sav;
SAVE IS fscores;

I encountered that the means and variances were slightly different from what I found in the strict invariance model. In this model, I also had the following message:

THE MODEL CONTAINS A NON-ZERO CORRELATION BETWEEN DEPENDENT VARIABLES.
SUCH CORRELATIONS ARE IGNORED IN THE COMPUTATION OF THE FACTOR SCORES.

I read that this has to do with having residual covariances in my WLSMV model. Could this be the reason why my factor means were different from those in the model, after I exported them?

Do you have another suggestion to obtain the factor scores and analyze mean differences adjusted for covariates?
 Linda K. Muthen posted on Tuesday, March 22, 2016 - 6:45 am
Factor score means are rarely the same as the factor means in the model because factor scores and factors are not the same.

Factor scores are not adjusted for covariates. The factor scores come from a model that contains covariates.
 Henrike Galenkamp posted on Wednesday, March 23, 2016 - 2:46 am
Thank you Linda,
What I forgot to mention is that the factor scores were from a model that did not contain the covariates.
Should the group means of these factor scores (without covariates) not be the same as the ones shown in my Mplus model (without covariates)?
 Linda K. Muthen posted on Wednesday, March 23, 2016 - 8:56 am
The same issue is relevant. Factor scores are not the same as the factors in a model unless factor score determinacy is one which is very unlikely to happen.