  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.
