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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 practicalintroduction to fitting LMMs in a Bayesian framework using the probabilisticprogramming language Stan. We choose Stan (rather than WinBUGS or JAGS) becauseit provides an elegant and scalable framework for fitting models in most of thestandard applications of LMMs. We ease the reader into fitting increasinglycomplex LMMs, first using a two-condition repeated measures self-paced readingstudy, followed by a more complex $2\times 2$ repeated measures factorialdesign that can be generalized to much more complex designs.

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