Fitting linear mixed models using JAGS and Stan: A tutorial

摘要

Psycholinguists routinely use linear mixed models (LMMs) for statistical inference. The most widely used tool for this purpose is the lmer function in the R library lme4. Although lmer has the advantage that models can be fit relatively quickly, one issue with this tool is that, when a full variance-covariance structure for variance components is defined, the model either fails to converge, or returns estimates of the correlation parameters that do not reflect the true underlying parameter values. LMMs fit using a Bayesian framework have several advantages over this conventional method: A full variance-covariance matrix for random effects can be defined even in cases where lmer would fail to converge or return nonsensical estimates; the underlying generative model can be flexibly changed; and, perhaps most importantly, a direct answer to the research question can be obtained by examining the posterior distribution given data. One major barrier to using Bayesian LMMs is that it is not obvious how to use the software available for Bayesian modeling. Although several good introductory books exist for Bayesian modeling in general, linear mixed modeling is typically treated in a fairly general way, and the more complex models that are used in psycholinguistics are usually not discussed. This tutorial provide a guide to allow researchers to quickly get started in fitting such models using the programming languages JAGS and Stan.