Advanced Bayesian Multilevel Modeling with the R Package brms

The brms package allows R users to easily specify a wide range of Bayesian single-level and multilevel models which are fit with the probabilistic programming language Stan behind the scenes.Several response distributions are supported, of which all parameters (e.g., location, scale, and shape) can be predicted.Non-linear relationships may be specified using non-linear predictor terms or semi-parametric approaches such as splines or Gaussian processes.Multivariate models can be fit as well.To make all of these modeling options possible in a multilevel framework, brms provides an intuitive and powerful formula syntax, which extends the well known formula syntax of lme4.The purpose of the present paper is to introduce this syntax in detail and to demonstrate its usefulness with four examples, each showing relevant aspects of the syntax.Stan comes with its own programming language, allowing for great modeling flexibility (Stan Development Team, 2017c;Carpenter et al., 2017).Many researchers may still be hesitant to use Stan directly, as every model has to be written, debugged, and possibly also optimized, which may be a time-consuming and error-prone process even for researchers familiar with Bayesian inference.The brms package (Bürkner, 2017) presented in this paper aims to remove these hurdles for a wide range of regression models by allowing the user to benefit from the merits of Stan by using extended lme4-like formula syntax (Bates et al., 2015), with which many R users are familiar.The brms package offers much more than writing efficient and human-readable Stan code.It comes with many post-processing