I have a question with regard to the different options for parametrization in Mplus when testing for measurement invariance. I thought there were two main options (to obtain identified models): - fix the latent factor mean to zero and the factor variance to one in each group OR - fix the first item mean to zero and the first item factor loading to one in each group(see example mentioned on http://www.ats.ucla.edu/stat/mplus/paperexamples/gregorich/)
However, is it also an option to fix the first item factor loading to one in each group but to constrain the first item mean to be equal across groups (instead of fixing it to zero), which seems to be the default in Mplus for multigroup CFA? Why would you choose to fix the first item mean to zero in each group instead of just constraining the means to be equal? Will this affect the results (e.g., the factor loadings) and how?