Bayesian Approaches to Regression and Mixed Effects Models Using brms

Session 1 – 03:00:00 – Bayesian linear models.
We begin by covering Bayesian linear regression. For this, we will use the brm command from the brms package, and we will compare and contrast the results with the standard lm command. By comparing and contrasting brm with lm we will see all the major similarities and differences between the Bayesian and classical approach to linear regression. We will, for example, see how Bayesian inference and model comparison works in practice and how it differs conceptually and practically from inference and model comparison in classical regression. As part of this coverage of linear models, we will also use categorical predictor variables and explore varying intercept and varying slope linear models.

Session 2 – 03:00:00 – Extending Bayesian linear models.
Classical normal linear models are based on strong assumptions that do not always hold in practice. For example, they assume a normal distribution of the residuals, and assume homogeneity of variance of this distribution across all values of the predictors. In Bayesian models, these assumptions are easily relaxed. For example, we will see how we can easily replace the normal distribution ofthe residuals with a t-distribution, which will allow for a regression model that is robust to outliers. Likewise, we can model the variance of the residuals as being dependent on values of predictor variables.

Session 3 – 03:00:00 – Bayesian generalized linear models.
Generalized linear models include models such as logistic regression, including multinomial and ordinal logistic regression, Poisson regression, negative binomial regression, zero-inflated models, and other models. Again, for these analyses we will use the brms package and explore this wide range of models using real world data-sets. In our coverage of this topic, we will see how powerful Bayesian methods are, allowing us to easily extend our models in different ways in order to handle a variety of problems and to use assumptions that are most appropriate for the data being modelled.

Session 4 – 03:00:00 – Multilevel and mixed models.
In this section, we will cover the multilevel and mixed effects variants of the regression models, i.e. linear, logistic, Poisson etc, that we have covered so far. In general, multilevel and mixed effects models arise whenever data are correlated due to membership of a group (or group of groups, and so on). For this, we use a wide range of real-world data-sets and problems, and move between linear, logistic, etc., models are we explore these analyses. We will pay particular attention to considering when and how to use varying slope and varying intercept models, and how to choose between maximal and minimal models. We will also see how Bayesian approaches to multilevel and mixed effects models can overcome some of the technical problems (e.g. lack of model convergence) that beset classical approaches.