Bayesian beta regressions with brms in R: A tutorial for phoneticians

Abstract

Phonetic research frequently involves analyzing numeric continuous outcome variables, such as durations, frequencies, loudness, and ratios. Another commonly used outcome type is proportions, including measures like the proportion of voicing during closure, gesture amplitude, and nasalance. Despite their bounded nature, proportions are often modeled using Gaussian regression, largely due to the default settings of commonly used statistical functions in R (e.g., lm() and lmer() from lme4). This practice persists in teaching and research, despite the fact that Gaussian models assume unbounded continuous data and may poorly fit proportion data. To address this issue, this tutorial introduces beta regression models, a more appropriate statistical approach for analyzing proportions. The beta distribution provides a flexible framework for modelling continuous data constrained between 0 and 1. The tutorial employs the brms package in R and assumes familiarity with regression modeling but no prior knowledge of Bayesian statistics. The tutorial includes two case studies illustrating the practical implementation of Bayesian beta regression models. Data and code are available athttps://github.com/stefanocoretta/beta-phon.