Measurement Invariance Testing Using Confirmatory Factor Analysis and Alignment Optimization: A Tutorial for Transparent Analysis Planning and Reporting

Measurement invariance—the notion that the measurement properties of a scale are equalacross groups, contexts, or time—is an important assumption underlying much of psychology research. The traditional approach for evaluating measurement invariance is to fit a series of nested measurement models using multiple-group confirmatory factor analyses. However, traditional approaches are strict, vary across the field in implementation, and present multiplicity challenges, even in the simplest case of two groups under study. The alignment method was recently proposed as an alternative approach. This method is more automated, requires fewer decisions from researchers, and accommodates two or more groups. However, it has different assumptions, estimation techniques, and limitations from traditional approaches. To address the lack of accessible resources that explain the methodological differences and complexities between the two approaches, we introduce and illustrate both, comparing them side by side. First, we overview the concepts, assumptions, advantages, and limitations of each approach. Based on this overview, we propose a list of four key considerations to help researchers decide which approach to choose and how to document their analytical decisions in a preregistration or analysis plan. We then demonstrate our key considerations on an illustrative research question using an open dataset and provide an example of a completed preregistration. Our illustrative example is accompanied by an annotated analysis report that shows readers, step-by-step, how to conduct measurement invariance tests using R and Mplus. Finally, we provide recommendations for how to decide between and use each approach and next steps for methodological research.