Hi Paul,

if you want to comapre the size of path coefficients (or covariances or whatever) across countriesyou have to establish strong measurement invariance first (e.g. equal loadings and equal intercepts). You can do this using Chi-Square Difference Test or Delta CFI criteria, there are several good explanantions how to do this in different software tools. 

You problably use the following stepwise approach:

1) test configural invariance - adaquate fit? - fine, otherwise modify your model and test again

2) week MI (metric MI): constrain loadings to be equal across groups, use Chi-Square Difference test or Delta CFI to descide if these contrains are tenable 

3) strong MI (scalar MI): add constrains on the itnercepts, corresponding intercepts should be equal across groups. use Chi-Square Difference test or Delta CFI to descide if these contrains are tenable (sometime partial invariacne can be reached, check some papers regarding this topic).

4) add contrains on you path coefficients

After you have established strong measurement invariance, you can add constraints on your path coefficients across groups, and see how the fit changes, angain, Chi-Square Difference Tests and Delta CFI criteria can guide your decision which contraints across countries is tenable. 

Establishing measurement invariance is critical, esspecially when you want to compare data from different countries. 

Best wishes, Manuel

Hi Paul,

You will use multi-group analysis?

If so, great. Because it is even clearer that it is possible to compare the adjustment indicators without performing measurement equivalence. In general, we do this equivalence when comparing different results using the GPA (Generalized Procrustes Analysis) with multidimensional scaling.

I compare the models of the theory of values using mainly Δχ² indicators, CAIC (Consistent Akaike information Criterion) and ECVI (Expected Cross Validation Index). When identified a statistically significant difference in Δχ² penalizes the model more c². And CAIC values and lower ECVI suggest a more suitable model.

In the article to test the children's values scale (attached) made this comparison (sorry, it's in Portuguese). But you can see the table where I compare the models. And has the Prof. Valdiney article (in English) that he does the same with the general values scale - BVS (attached).

Good job Paul!! =)

Hi Paul,

if you want to comapre the size of path coefficients (or covariances or whatever) across countriesyou have to establish strong measurement invariance first (e.g. equal loadings and equal intercepts). You can do this using Chi-Square Difference Test or Delta CFI criteria, there are several good explanantions how to do this in different software tools. 

You problably use the following stepwise approach:

1) test configural invariance - adaquate fit? - fine, otherwise modify your model and test again

2) week MI (metric MI): constrain loadings to be equal across groups, use Chi-Square Difference test or Delta CFI to descide if these contrains are tenable 

3) strong MI (scalar MI): add constrains on the itnercepts, corresponding intercepts should be equal across groups. use Chi-Square Difference test or Delta CFI to descide if these contrains are tenable (sometime partial invariacne can be reached, check some papers regarding this topic).

4) add contrains on you path coefficients

After you have established strong measurement invariance, you can add constraints on your path coefficients across groups, and see how the fit changes, angain, Chi-Square Difference Tests and Delta CFI criteria can guide your decision which contraints across countries is tenable. 

Establishing measurement invariance is critical, esspecially when you want to compare data from different countries. 

Best wishes, Manuel

Manuel has provided an excellent description of invariance but these models used to be tiresome to specify and do the model testingthat Ana described. The latest version of Mplus has 'black boxed' all these tasks which makes things very easy (as long as you understand what it's doing).

Thanks for this Mark.

I agree that doing this in Amos may be quite tiresome. I do the analyses in R with the packages lavaan and semTools, which is also pretty straight forward.