# Comparing Bayesian random coefficient prediction and latent interaction models for multilevel moderated mediation

## TL;DR

This study compares two Bayesian models for analyzing moderated mediation in hierarchical data and finds they perform similarly, with one being slightly better for small samples.

## Contribution

The paper provides a comparative evaluation of BRCP and BINT models for moderated mediation in multilevel contexts.

## Key findings

- BRCP and BINT models produced highly similar parameter estimates with negligible differences.
- Both models showed acceptable bias and controlled Type I error rates, except for small cluster sizes.
- BRCP is slightly more suitable for smaller samples due to lower bias compared to BINT.

## Abstract

This study compares Bayesian random coefficient prediction (BRCP) and Bayesian latent interaction (BINT) models to detect moderated mediation effects in multilevel contexts.

We evaluated the performance of these models under various conditions using empirical data from the Trends in International Mathematics and Science Study (TIMSS2019) dataset and simulated data.

The results showed that the BRCP and BINT models produced highly similar parameter estimates with negligible differences.

The empirical findings revealed consistent within- and between-level relationships across both models, while simulation results indicated acceptable bias, controlled Type I error rates, and sufficient power in most conditions, except for smaller cluster sizes. We observed a slightly higher bias for BINT under small sample conditions. Overall, both models are effective for moderated mediation analysis, though BRCP is slightly more suitable for smaller samples.

These findings highlight the robustness of Bayesian approaches in handling complex hierarchical data, particularly in educational and psychological research. Future research should explore additional factors, such as measurement error and more complex moderator structures, to enhance our understanding of Bayesian multilevel modeling.