Ex. 2.1, step 7: Conclusion
To test the cross-time and cross-country comparability of the anti-immigration scale, we estimated a series of multi-group models with different sets of parameters constrained. The analysis showed that a model with equal factor loadings and intercepts - i.e. full scalar equivalence - fitted the data reasonably well. However, closer inspection of modification indices and expected parameters changes showed that some of the equality constraints for one of the items, namely IMSMETN, were not tenable. The model was re-estimated without these constraints on IMSMETN and model fit improved substantially.
These results indicate that our scale has the characteristic of partial scalar equivalence: for at least two items, factor loadings and intercepts are equal across the groups. It is therefore justified to compare means for the latent variable over all time points and countries in the study. In other words, our measurements are sufficiently comparable to continue the substantive analysis1.
-  Ideally, we would continue the analyses with the scores for the latent variable. This is exactly what was done by Meuleman et al. (2009). In the remainder of this module, however, we will work with a sum scale based on the items instead. The use of this sum scale has the disadvantage that it does not correct for the fact that we only found partial and not full equivalence. However, this approach makes it possible for students with no interest in the topic of measurement equivalence to skip Chapter 2.