Advanced Bayesian Multilevel Modeling with the R Package brms

Advanced Bayesian Multilevel Modeling with the R Package brms

Vol. XX/YY, AAAA 20ZZ | Paul-Christian Bürkner
The brms package in R provides a flexible framework for Bayesian multilevel modeling, allowing users to fit a wide range of single-level and multilevel models using the probabilistic programming language Stan. It supports various response distributions, enabling distributional regression where all parameters of the response distribution can be predicted simultaneously. Non-linear relationships can be modeled using non-linear predictor terms or semi-parametric approaches like splines or Gaussian processes. brms extends the well-known formula syntax of lme4, offering an intuitive and powerful way to specify complex models. The paper introduces this syntax in detail and demonstrates its usefulness through four examples, each highlighting different aspects of the syntax. The package allows for the prediction of all response parameters, including location, scale, and shape, and supports non-linear models, generalized additive models, and multi-membership models. It also includes post-processing and visualization functions for posterior predictive checks, cross-validation, and effect visualization. The paper discusses the advantages of the Bayesian framework, including the ability to derive probability statements and incorporate prior knowledge. brms aims to simplify the use of Stan by providing an extended lme4-like formula syntax, making it accessible to a broader audience. The package has replaced and extended the functionality of many other R packages, offering a comprehensive solution for regression modeling. The paper also outlines future developments, including extended multivariate models and missing value imputation.The brms package in R provides a flexible framework for Bayesian multilevel modeling, allowing users to fit a wide range of single-level and multilevel models using the probabilistic programming language Stan. It supports various response distributions, enabling distributional regression where all parameters of the response distribution can be predicted simultaneously. Non-linear relationships can be modeled using non-linear predictor terms or semi-parametric approaches like splines or Gaussian processes. brms extends the well-known formula syntax of lme4, offering an intuitive and powerful way to specify complex models. The paper introduces this syntax in detail and demonstrates its usefulness through four examples, each highlighting different aspects of the syntax. The package allows for the prediction of all response parameters, including location, scale, and shape, and supports non-linear models, generalized additive models, and multi-membership models. It also includes post-processing and visualization functions for posterior predictive checks, cross-validation, and effect visualization. The paper discusses the advantages of the Bayesian framework, including the ability to derive probability statements and incorporate prior knowledge. brms aims to simplify the use of Stan by providing an extended lme4-like formula syntax, making it accessible to a broader audience. The package has replaced and extended the functionality of many other R packages, offering a comprehensive solution for regression modeling. The paper also outlines future developments, including extended multivariate models and missing value imputation.
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