Building a simpler moderated nonlinear factor analysis model with Markov Chain Monte Carlo estimation

Moderated nonlinear factor analysis (MNLFA) has emerged as an important and flexible data analysis tool, particularly in integrative data analysis setting and psychometric studies of measurement invariance and differential item functioning. Substantive applications abound in the literature and span a broad range of disciplines. MNLFA unifies item response theory, multiple group, and multiple indicator multiple cause modeling traditions, and it extends these frameworks by conceptualizing latent variable heterogeneity as a source of differential item functioning. The purpose of this article was to illustrate a flexible Markov chain Monte Carlo-based approach to MNLFA that offers statistical and practical enhancements to likelihood-based estimation while remaining plug and play with established analytic practices. Among other things, these enhancements include (a) missing data handling functionality for incomplete moderators, (b) multiply imputed factor score estimates that integrate into existing multiple imputation inferential methods, (c) support for common data types, including normal/continuous, nonnormal/continuous, binary, ordinal, multicategorical nominal, count, and two-part constructions for floor and ceiling effects, (d) novel residual diagnostics for identifying potential sources of differential item function, (e) manifest-by-latent variable interaction effects that replace complex moderation function constraints, and (f) integration with familiar regression modeling strategies, including graphical diagnostics. A real data analysis example using the Blimp software application illustrates these features. (PsycInfo Database Record (c) 2025 APA, all rights reserved).