MultiLevelOptimalBayes: Regularized Bayesian Estimator for Two-Level Latent Variable Models

Implements a regularized Bayesian estimator that optimizes the estimation of between-group coefficients for multilevel latent variable models by minimizing mean squared error (MSE) and balancing variance and bias. The package provides more reliable estimates in scenarios with limited data, offering a robust solution for accurate parameter estimation in two-level latent variable models. It is designed for researchers in psychology, education, and related fields who face challenges in estimating between-group effects under small sample sizes and low intraclass correlation coefficients. The package includes comprehensive S3 methods for result objects: print(), summary(), coef(), se(), vcov(), confint(), as.data.frame(), dim(), length(), names(), and update() for enhanced usability and integration with standard R workflows. Dashuk et al. (2025a) <doi:10.1017/psy.2025.10045> derived the optimal regularized Bayesian estimator; Dashuk et al. (2025b) <doi:10.1007/s41237-025-00264-7> extended it to the multivariate case; and Luedtke et al. (2008) <doi:10.1037/a0012869> formalized the two-level latent variable framework.

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