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. Translational Abstract In the field of psychology, questionnaires or tests are often used to measure latent constructs like cognition or attitude. In order to meaningfully compare observed scores derived from these measurement instruments, it is crucial that the construct is measured equivalently across individuals. This condition is also referred to as measurement invariance. Most recently, moderated nonlinear factor analysis (MNLFA) has been proposed as a method to assess measurement invariance. The advantage of this method over more traditional methods is that it assesses measurement invariance in a more flexible way. The majority of guidelines on how to perform MNLFA, however, involve commercial statistical software. In this article, we demonstrate how MNLFA can be applied in R. Our aim is to make MNLFA more accessible to researchers or practitioners without access to commercial statistical software.