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

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.

Submitted to Psychological Methods (Special Issue on Bayesian Data Analysis); 30 pages; 6 figures

References in corpus (3)

• Balancing Type I Error and Power in Linear Mixed Models
• Parsimonious Mixed Models
• Statistical methods for linguistic research: Foundational Ideas - Part II

Cited by in corpus (6)

• Balancing Type I Error and Power in Linear Mixed Models
• Statistical methods for linguistic research: Foundational Ideas - Part II
• Statistical methods for linguistic research: Foundational Ideas - Part I
• SEAM: An Integrated Activation-Coupled Model of Sentence Processing and Eye Movements in Reading
• Confronting Quasi-Separation in Logistic Mixed Effects for Linguistic Data: A Bayesian Approach
• Bayesian Hierarchical Modelling for Tailoring Metric Thresholds