The issue of measurement invariance commonly arises in factor-analytic contexts, with methods for assessment including likelihood ratio tests, Lagrange multiplier tests, and Wald tests. These tests all require advance definition of the number of groups, group membership, and offending model...

Researchers are often interested in testing for measurement invariance with respect to an ordinal auxiliary variable such as age group, income class, or school grade. In a factor-analytic context, these tests are traditionally carried out via a likelihood ratio test statistic comparing a model...