Barreda S, Silbert N. Bayesian Multilevel Models for Repeated Measures data: A Conceptual and Practical Introduction in R

Routledge, 2023. — 485 p. — ISBN 978-1-032-25962-8.Байесовские многоуровневые модели для данных повторных измерений: концептуальное и практическое введение в R
This book presents an introduction to the statistical analysis of repeated measures data using Bayesian multilevel regression models. Our approach is to fit these models using the brms package and the Stan programming language in R. This book introduces mathematical and modeling concepts in plain English, and focuses on understanding the visual/geometric consequences of different regression model structures rather than on rigorous mathematical explanations of these.Statistical modeling is as much a coding challenge as it is a mathematical challenge. As any programmer with some experience knows, copying existing scripts and modifying them slightly is an excellent way to learn to code, and often a new skill can be learned shortly after an understandable example can be found. To that end, rather than use a different toy data set for every new topic introduced, this book presents a set of fully worked analyses involving increasingly complicated models fit to the same experimental data.
In this book, the authors offer an introduction to statistics entirely focused on repeated measures data beginning with very simple two-group comparisons and ending with multinomial regression models with many ‘random effects’. Across 13 well-structured chapters, readers are provided with all the code necessary to run all the analyses and make all the plots in the book, as well as useful examples of how to interpret and write-up their own analyses.This book provides an accessible introduction for readers in any field, with any level of statistical background. Senior undergraduate students, graduate students, and experienced researchers looking to ‘translate’ their skills with more traditional models to a Bayesian framework, will benefit greatly from the lessons in this text.1 Introduction: Experiments and variables
2 Probabilities, likelihood, and inference
3 Fitting Bayesian regression models with brms
4 Inspecting a ‘single group’ of observations using a Bayesian multilevel model
5 Comparing two groups of observations: Factors and contrasts
6 Variation in parameters (‘random effects’) and model comparison
7 Comparing many groups, interactions, and posterior predictive checks
8 Varying variances, more about priors, and prior predictive checks
9 Quantitative predictors and their interactions with factors
10 Logistic regression and signal detection theory models
11 Multiple quantitative predictors, dealing with large models, and Bayesian ANOVA
12 Multinomial and ordinal regression
13 Writing up experiments: An investigation of the perception of apparent speaker characteristics from speech acoustics