PCLVMthesis implements Partially Confirmatory Latent Variable Modelling (PCLVM) developed for Zhang Yifan’s PhD thesis:
Bayesian Regularization for Latent Variable Modeling: A Unified Framework and Prior Comparison
The methodological foundation builds upon the pcfa function from the LAWBL package. The current implementation re-engineers the estimation procedure using C++ improved computational efficiency and scalability, while introducing substantial extensions in model structure and estimation strategy. The R6-based interface provides a user-friendly front-end, while the underlying Rcpp module performs posterior sampling and matrix operations efficiently, ensuring extensibility and computational robustness.
Applies regularization to all major components of the factor model, including factor loadings, latent factor covariance matrices, and residual covariance matrices, with graphical regularization used for covariance structures when appropriate.
Supports partially confirmatory loading specifications through a user-defined design matrix Q, enabling structured theoretical constraints alongside regularized estimation.
Provides flexible latent factor structure modeling through full or block-specific Inverse-Wishart priors, full or block-specific covariance shrinkage, and partial regularization on selected correlation blocks combined with Inverse-Wishart estimation.
Offers multiple shrinkage prior choices for each model component, including Lasso, Horseshoe, and Spike-and-Slab (SSP), with independent user control over prior specification across parameter blocks.
Accommodates multiple latent variable structures, including standard CFA, bifactor models, MTMM models, and testlet effect models within a unified partially confirmatory framework.
Supports ordinal indicators, mixed measurement scales, and missing data handling through Bayesian data augmentation.
These capabilities allow structured theoretical specifications and data-driven shrinkage to coexist within a unified Bayesian framework for latent variable modeling.
# install.packages("devtools")
devtools::install_github("ZhangYifan-Jenny/PCLVMthesis")Please refer to the online tutorial for more comprehensive examples.
Zhang, Y. (PhD Thesis). Bayesian Regularization for Latent Variable Modeling: A Unified Framework and Prior Comparison.
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.
Chen, J. (2020). A partially confirmatory approach to the multidimensional item response theory with the Bayesian Lasso. Psychometrika. 85(3), 738-774. DOI: 10.1007/s11336-020-09724-3.
LAWBL Package: https://jinsong-chen.github.io/LAWBL/index.html