A non-linear Bayesian approach to examine the development of Brazilian Portuguese (L3) vowels by an Argentinean learner

Abstract This chapter presents a methodological contribution to language development research from a Complex Dynamic Systems Theory (CDST) perspective by implementing Bayesian Generalized Additive Mixed Models (GAMMs). We illustrate this approach with a case study on the longitudinal development of Brazilian Portuguese (BP) vowels by an Argentinean learner (L1: Spanish; L2: English; L3: BP). Acoustic data (F1 and F2 values) collected over a year show how Bayesian GAMMs capture non-linear developmental trajectories and dynamic phonological changes. Unlike traditional models, Bayesian GAMMs account for uncertainty and align with CDST principles by modeling gradual, individualized change over time. We discuss the affordances of this approach for process-oriented research, advocating for its adoption in studies that model complexity and variability in language development.