Bayesian SEM

Zhang, Y., & Chen, J. (2024). Accommodating and Extending Various Models for Special Effects Within the Generalized Partially Confirmatory Factor Analysis Framework. Applied Psychological Measurement, 48(4-5), 208-229. [doi] Artile

Presented at 2023 National Council on Measurement in Education Presentation Poster

Special measurement effects including the method and testlet effects are common issues in educational and psychological measurement. They are typically covered by various bifactor models or models for the multiple traits multiple methods (MTMM) structure for continuous data and by various testlet effect models for categorical data. However, existing models have some limitations in accommodating different type of effects. With slight modification, the generalized partially confirmatory factor analysis (GPCFA) framework can flexibly accommodate special effects for continuous and categorical cases with added benefits. Various bifactor, MTMM and testlet effect models can be linked to different variants of the revised GPCFA model. Compared to existing approaches, GPCFA offers multidimensionality for both the general and effect factors (or traits) and can address local dependence, mixed-type formats, and missingness jointly. Moreover, the partially confirmatory approach allows for regularization of the loading patterns, resulting in a simpler structure in both the general and special parts. We also provide a subroutine to compute the equivalent effect size. Simulation studies and real-data examples are used to demonstrate the performance and usefulness of the proposed approach under different situations.

Chen, J., & Zhang, Y. (2024). Research Design and Model Estimation Under the Partially Confirmatory Latent Variable Modeling Framework with Multi-Univariate Bayesian Lassos. Structural Equation Modeling: A Multidisciplinary Journal, 1–15. [doi] Artile

This research builds upon existing developments of the partially confirmatory approach by introducing predictors and regularizations to two additional parameter matrices: structural and differential coefficients. The outcome is a comprehensive framework called partially confirmatory latent variable modeling (PCLVM), where researchers can apply different regularizations to four parameter matrices individually or collectively, and in full or in part. With PCLVM, applied researchers can design a variety of research studies for different purposes, depending on the combinations of different regularizations. It employs a mixed estimation algorithm combining univariate and multivariate Bayesian Lassos for measurement- and structural-level regularizations with or without correlated residuals. The attractiveness of the proposed framework was demonstrated through a variety of typical cases that can be readily estimated and widely encountered in practice. Simulation studies and real-life data analysis were adopted to showcase the performance and versatility of PCLVM and its comparisons with exploratory structural equation modeling.