Bayesian Penalty Methods for Evaluating Measurement Invariance in Moderated Nonlinear Factor Analysis - Holger Brandt, Siyuan Marco Chen and Daniel J. Bauer
In this paper we propose the application of Bayesian Moderated Nonlinear Factor Analysis to overcome limitations of traditional approaches to detect DIF. We investigate how modern Bayesian shrinkage priors can be used to identify DIF items in situations with many groups and continuous covariates. We compare the performance of lasso-type, spike-and-slab, and global-local shrinkage priors (e.g., horseshoe) to standard normal and small variance priors. Results indicate that spike-and-slab and lasso priors outperform the other priors. Horseshoe priors provide slightly lower power compared to lasso and spike-andslab priors. Small variance priors result in very low power to detect DIF with sample sizes below 800, and normal priors may produce severely inflated type I error rates. We illustrate the approach with data from the PISA 2018 study.
Software/Packages Required:
R studio/JAGS