Dear Çinar,

There are many pieces of literature about this. For the importance of measurement invariance, you may have a look at :

When does measurement invariance matter?

D Borsboom

Medical care 44 (11), S176-S181

For a guideline of how to conduct and what to report you may have a look at :

A checklist for testing measurement invariance

R Van de Schoot, P Lugtig, J Hox

European Journal of Developmental Psychology 9 (4), 486-492

You may also have a look at the Mplus user guide (attached) Chapter 5, which has a great explain about MIMIC analysis. There plenty of literature about that, especially with you look at IRT, under the dysfunction item analysis (DIF). 

For a syntax to Prelis, I'm afraid that I cannot help you since I use MPLUS. It is possible to conduct such analysis in R and AMOS. 

I hope this help you out. 

Kindest regards,

Dear Çinar,

There are two methods to evaluate invariance in CFA (actually, there is a third way, that is multilevel SEM, but that is not your case).

The firs one is multiple groups CFA, the second is MIMIC modeling.

In multi-group CFA the analysis involves two separate input matrices that are simultaneously analysed (one for males and one for females). A researcher can put constraints to the parameters (e.g. equal factor loadings) in order to examine the equivalence of the measurement model. A precious advantage of multi-group CFA is that all parameters to test measurement invariance and population heterogeneity can be examined (i.e., factor loadings, intercepts, residual variances, factor variances, factor covariances, latent means).

Instead, MIMIC involves the analysis of a single covariance matrix and in your case comprises the inclusion of a dummy variable for the gender. After a satisfactory measurement model has been specified, you can regress latent variable(s) and indicators onto the dummy variable. A significant effect on latent variables indicates a difference between groups on latent means, instead a significant effect on indicators indicates lack of measurement invariance (the items work in a different way in the two groups).

Personally I prefer multi-group CFA since it allows to check all the aspects of measurement invariance.  

 If you do not have measurement invariance, you cannot say anything about differences in the latent means between the two groups. There are different levels of measurement invariance.

For different levels of measurement invariance you may have a look at:

Meredith, W. (1993). Measurement invariance, factor analysis and factorial     invariance. Psychometrika, 58, 525–543.

All the best,

Gianmaria

Hi, you could do an omnibus test on the indicator covariance matrices. If this test results in a non-significant chi-square test then all forms of invariances (e.g., metric invariance) will hold. However, this is a very rigid test. Hence testing for metric invariance and - depending on your research goal - other forms would be an alternative (or follow up procedures once the omnibus test is significant).

Best,

Holger

Thanks to the guidance and encouragement from the previous replies, I have managed to perform a multigroup SEM in AMOS software. Yet as far as I understood, the program yielded estimates and fit indices for split samples of males and females. I could do this by PRELIS working on the split samples. Could you please indicate what coefficients should I check for the "difference" of the two groups in terms of model fit in AMOS?