The MACS approach to testing for multigroup invariance of a second-order structure: A walk through the process

The overarching intent of this article is to exemplify strategies associated with tests for measurement invariance that are uncommonly applied and reported in the extant literature. Designed within a pedagogical framework, the primary purposes are 3-fold and illustrate (a) tests for measurement invariance based on the analysis of means and covariance structures (MACS), (b) use of the MACS approach in testing for an invariant higher order factor structure, and (c) tests for latent mean differences relative to both levels of a higher order factor structure. Addressing additional application limitations, the secondary purposes are 2-fold and illustrate (a) determination of invariance based on two substantially different sets of criteria and (b) interpretation of noninvariant measurement items within the context of an item response theory perspective. We are hopeful that readers will find the didactic approach to be helpful in gaining a better understanding of the invariance-testing process.