Bayesian linear mixed models using Stan: A tutorial for psychologists, linguists, and cognitive scientists

TL;DR

This tutorial introduces Bayesian linear mixed models using Stan, guiding psychologists, linguists, and cognitive scientists through practical steps from simple to complex models in a scalable probabilistic programming environment.

Contribution

It provides a practical, step-by-step tutorial for fitting Bayesian linear mixed models in Stan tailored for researchers in psychology, linguistics, and cognitive science.

Findings

Demonstrates fitting simple and complex LMMs in Stan

Shows how to handle factorial designs in Bayesian LMMs

Provides accessible guidance for researchers new to Bayesian modeling

Abstract

With the arrival of the R packages nlme and lme4, linear mixed models (LMMs) have come to be widely used in experimentally-driven areas like psychology, linguistics, and cognitive science. This tutorial provides a practical introduction to fitting LMMs in a Bayesian framework using the probabilistic programming language Stan. We choose Stan (rather than WinBUGS or JAGS) because it provides an elegant and scalable framework for fitting models in most of the standard applications of LMMs. We ease the reader into fitting increasingly complex LMMs, first using a two-condition repeated measures self-paced reading study, followed by a more complex $2\times 2$ repeated measures factorial design that can be generalized to much more complex designs.