Decoding the Meaning of Factorial Invariance and Updating the Practice of Multi-group Confirmatory Factor Analysis: A Demonstration With TIMSS Data

Measurement invariance (MI) has been developed in a very technical language and manner that is generally not widely accessible to social and behavioral researchers and applied measurement specialists. Primarily relying on the widely known concepts in regression and linear statistical modeling, this paper decoded the concept of MI in the context of factor analysis. The paper began by describing what is MI (and lack of MI) and how the concept can be realized in the context of factor analysis. Next, we explained the need for modeling the mean and covariance structure (MACS), instead of the traditionally applied covariance structure, in detecting factorial invariance. Along the way, we addressed the related matter…