29 March 2019
Bayesian Multilevel Modelling
This course provides a general introduction to Bayesian multilevel modelling. Throughout, we will extensively use R and the Bayesian probabilistic programming language Stan and its R based brms interface. The course begins by providing a solid introduction to all the fundamental principles and concepts of Bayesian data analysis: the likelihood function, prior distributions, posterior distributions, high posterior density intervals, posterior predictive distributions, marginal likelihoods, Bayes factors, etc. We will do this using some simple models that are easy to understand and easy to work with. We then turn to providing a solid introduction to multilevel models, again beginning with conceptually and computationally simple multilevel models. We then proceed to more practically useful Bayesian multilevel models, and ones that necessarily require Monte Carlo methods, particularly multilevel general and generalized linear regression models. For these models and analyses, we will make extensive use of the R based brms interface to Stan, which allows general Bayesian multilevel regression to be done remarkably easily. As part of the introduction to multilevel regression, we will ensure that we first have a solid understanding of the (non-multilevel) general and generalized linear models. In final part of the course will cover multilevel models that are not regression models per se. In particular, we will explore multilevel probabilistic mixture models, especially Latent Dirichlet Allocation and the Hierarchical Dirichlet Process model, which have been shown to be particularly valuable in the modelling of text data. Throughout the course, we will have interludes where we address some major general issues in Bayesian data analysis, particularly Markov Chain Monte Carlo methods and Bayesian model evaluation (e.g., using cross-validation, WAIC, and Bayes factors, etc).
Mark Andrews is a Senior Lecturer in the Psychology Department at Nottingham Trent University in Nottingham, England. Mark is a graduate of the National University of Ireland and obtained an MA and PhD from Cornell University in New York. Mark's research
Participants will find the course useful if they
- Currently work with multilevel models such multilevel linear regression (also known as linear mixed effects models) and wish to learn more about Bayesian approaches to these models.
- Currently work with, or wish to learn more about, extensions to the multilevel linear models, including multilevel logistic, Poisson, etc regression, and especially how to perform Bayesian analyses of these models.
- Wish to learn more about the theoretical basis of multilevel modelling.
- Wish to learn more about Bayesian data analysis generally.
- Wish to learn how to use Bayesian probabilistic modelling languages such as Stan, and the R based brms interface to Stan.
Participants need only have experience in the usual range and repertoire of statistical methods that are typically taught in undergraduate social science courses. This would include familiarity with classical (i.e. frequentist or sampling theory based) inference using hypothesis tests, p-values, and confidence intervals; familiarity with (multiple) linear regression, t-tests, analysis of variance models, etc. Expertise or extensive experience with R is not required, but a minimal familiarity with R (as might be obtained from online video tutorials) would be helpful. No experience whatsoever with Bayesian analysis is required, nor is any experience with multilevel modelling.
By the end of the course participants will
- Understand the general principles of Bayesian data analysis.
- Understand the theoretical basis of multilevel models.
- Understand, and be able to perform, Bayesian analyses of multilevel general and generalized linear models.
- Understand, and be able to perform, Bayesian model evaluation.
- Be able to perform Bayesian data analysis using R, the probabilistic modelling language Stan, and the brms interface.
PhD students have the opportunity to receive European Credit Transfer System (ECTS) points thanks to our cooperation with the Cologne Graduate School in Management, Economics and Social Sciences of the University of Cologne. You will be charged an administration fee of EUR 50,00 (3 ECTS points).
EUR 300: Student/PhD student rate.
EUR 450: Academic/non-profit/public sector rate.
The course fee includes lectures and course materials as well as coffee breaks and social events. Accommodation and meals are not included.