Regularized Bayesian Estimator for Two-Level Latent Variable Models.
MultiLevelOptimalBayes
MultiLevelOptimalBayes (MLOB) 
MLOB is an R package for estimating between-group effects in multilevel latent variable models using an optimally regularized Bayesian estimator. It is especially useful for small-sample settings, low ICC data, and hierarchical models commonly used in psychology, education, and social sciences.
Features
- Regularized Bayesian estimator optimized for minimum mean squared error (MSE)
- Robust to small sample sizes and low intraclass correlation (ICC)
- Supports covariate adjustment and group-level balancing
- Optional jackknife resampling for improved CI coverage
- Returns full inferential output: point estimates, standard errors, p-values, and confidence intervals
- Clean and user-friendly interface via the
mlob()function
Installation
To install the development version from GitHub:
install.packages("devtools")
devtools::install_github("MLOB-dev/MLOB")
MLOB is available on CRAN under the GPL-3 license. To install the released version:
install.packages("MultiLevelOptimalBayes")
View the Vignette
After installing the package, run the following to open the introductory vignette:
vignette("MultiLevelOptimalBayes-Intro")
Examples
library(MultiLevelOptimalBayes)
Fit a model on the iris dataset
result <- mlob(Sepal.Length ~ Sepal.Width + Petal.Length, data = iris,
group = "Species", conf.level = 0.95)
View results
summary(result)
Limitations
-The estimator assumes approximately equal group sizes. Although balancing helps, unequal sizes may still bias results.
Grid-search is local around the ML estimate; global optimum is found with high probability but is not guaranteed.
Jackknife resampling improves inference in small samples but can be computationally heavy in larger samples.
Currently supports two-level models with continuous outcomes only. Extensions to GLMMs or 3+ level models are future work.
Contributing & Support
Please open an issue at:
https://github.com/MLOB-dev/MLOB/issues
Users may also join discussions or suggest enhancements on the Discussions page at
https://github.com/MLOB-dev/MLOB/discussions.
Authors
Valerii Dashuk
Binayak Timilsina
Martin Hecht
Steffen Zitzmann
Citation
If you use MLOB in your research, please cite:
Dashuk, V., Hecht, M., Luedtke, O., Robitzsch, A., & Zitzmann, S. (2024). An Optimally Regularized Estimator of Multilevel Latent Variable Models, with Improved MSE Performance https://doi.org/10.13140/RG.2.2.18148.39048