Assessing measurement invariance with moderated nonlinear factor analysis using the R package OpenMx

Assessing measurement invariance is an important step in establishing a meaningful comparison of measurements of a latent construct across individuals or groups. Most recently, moderated nonlinear factor analysis (MNLFA) has been proposed as a method to assess measurement invariance. In MNLFA models, measurement invariance is examined in a single-group confirmatory factor analysis model by means of parameter moderation. The advantages of MNLFA over other methods is that it (a) accommodates the assessment of measurement invariance across multiple continuous and categorical background variables and (b) accounts for heteroskedasticity by allowing the factor and residual variances to differ as a function of the background variables. In this article, we aim to make MNLFA more accessible to researchers without access to commercial structural equation modeling software by demonstrating how this method can be applied with the open-source R package OpenMx.