When you translated an instrument, you still do not know if the translated instrument will work in the same way as the original. Measurement invariance is a procedure to test the equivalency of tests across various samples and situations. It can be used to test the test equivalency between the original and the translated tests. Based on my experience, however, most translated measures are used without this critical validation procedure. Reviewers' comment implies other issues, but measurement invariance is often an issue in a context as yours.

Thanks Simon, do you also suggest to get latent mean differences?

Based on your response, i believe you are familiar with MI. Latent mean difference testing is not necessary to show the test equivalency. In fact, depending on your hypothesis, you sometimes expect latent mean differences (e.g., an experimental study). Configural and metric invariance tests might be necessary to show test equivalency across the samples.

I suggest to always increase the information you are giving. Not making a simple validation, add a measurement invariance, an IRT analysis or something else.

Also, if you have some high-ranked journal of the country, they normally like this as well as if the diferent scales versions are in the same journal.

Dear Laura,

Thanks, I have added the measurement invariance and I will check for Rasch .

Daniel, I am curious why anyone would use PCA for the purpose of factor analysis. If you are familiar with any recent development, can you provide more information?

Thank you in advance!