# An Optimally Regularized Estimator of Multilevel Latent Variable Models with Improved MSE Performance

## TL;DR

This paper introduces a new Bayesian estimator for multilevel models that improves accuracy, especially in small datasets with low correlations.

## Contribution

The paper presents an optimally regularized Bayesian estimator that outperforms traditional maximum likelihood in mean squared error.

## Key findings

- The estimator shows improved MSE performance in small samples with low ICCs.
- Computer simulations confirm the estimator's effectiveness across varying group sizes and correlations.

## Abstract

We propose an optimally regularized Bayesian estimator of multilevel latent variable models that aims to outperform traditional maximum likelihood (ML) estimation in mean squared error (MSE) performance. We focus on the between-group slope in a two-level model with a latent covariate. Our estimator combines prior information with data-driven insights for optimal parameter estimation. We present a “proof of concept” by computer simulations, involving varying numbers of groups, group sizes, and intraclass correlations (ICCs), which we conducted to compare the newly proposed estimator with ML. Additionally, we provide a step-by-step tutorial on applying the regularized Bayesian estimator to real-world data using our MultiLevelOptimalBayes package.

Encouragingly, our results show that our estimator offers improved MSE performance, especially in small samples with low ICCs. These findings suggest that the estimator can be an effective means for enhancing estimation accuracy.