A Tutorial on Assessing Measurement Invariance with Moderated (Non-)Linear Factor Analysis in JASP

In confirmatory factor analysis, measurement invariance is needed both to ensure that a questionnaire measures individuals equivalently across covariates (e.g., age, gender) and to justify interpreting any differences in latent factor means or relations as substantive rather than artefactual. Commonly, measurement invariance is investigated by turning (often continuous) covariates into categories and then use multi-group confirmatory factor analysis (MGCFA) in a structural equation modeling framework. However, this practice discards information and can undermine the validity of conclusions about measurement invariance and differential item functioning. Moderated (Non-)linear Factor Analysis (MNLFA) overcomes these limitations by allowing both continuous and categorical covariates to act as moderators of any parameter in a latent factor model. This allows to study measurement invariance and differential item functioning without discretizing covariates. However, current implementations of MNLFA require complex code in R or commercial software (Mplus), and do not have intuitive point-and-click user interfaces. To make MNLFA accessible to a broad range of applied researchers, we have implemented it in the free, open-source software JASP and provide a step-by-step tutorial on assessing measurement invariance using MNLFA in JASP. This implementation allows researchers to conduct more precise and informative invariance analyses without extensive programming effort.