Workshop: Bayesian Estimation for Multilevel Models: Overcoming Computational Hurdles and Enhancing Statistical Inference

The analysis of longitudinal data often requires multilevel models that can handle complex structures, numerous random effects, and non-normal outcomes. In these scenarios, traditional maximum likelihood (ML) estimation is increasingly prone to convergence failures. This day-long, practical, hand-on workshop introduces Bayesian estimation as the essential alternative for the modern psychological scientist, bridging the gap between computational necessity and theoretical clarity. We will examine the rise of ""computational frequentism,"" where researchers adopt Bayesian methods to resolve practically the limitations of ML in several contexts. We will then pivot to the substantive benefits of the Bayesian framework. Participants will learn how combining prior information with likelihood functions creates posterior distributions that offer richer, more intuitive insights than standard frequentist point estimates.

****Key learning objectives:
1. Solving Convergence Issues: Strategies for using Bayesian estimators for complex multilevel models.
2. Epistemological Clarity: Moving beyond the limitations of null-hypothesis significance testing to making probability statements about hypotheses.
3. Practical Application: A tutorial on specifying models in R (brms) and Mplus, covering prior specification, posterior interpretation, and reporting standards (e.g., Highest Density Intervals).
Lecture notes, example datasets, and analysis code will be made available.

Suggested Readings:
Laurenceau, J.-P., DiGiovanni, A. M., & Bolger, N. (2026). Intensive longitudinal methods: Toward a psychological science of daily life. Annual Review of Psychology, 77, 513–
541. https://doi.org/10.1146/annurev-psych-040325-025418
Levy, R, & McNeish, D. (2023). Perspectives on Bayesian inference and their implications for data analysis. Psychological Methods, 28(3), 719–39. https://doi.org/10.1037/met0000443

--->Prerequisites:
1) bring a laptop with R (brms) and the free demo version of Mplus pre-loaded to follow along;
2) have good working knowledge of multiple regression and ideally some working knowledge of standard frequentist multilevel modeling (MLM).