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In:Research Methods in Complex Dynamic Systems Theory Approaches to Second Language Development
Edited by Wander Lowie, Rosmawati and Vanessa De Wilde
[Research Methods in Applied Linguistics 14] 2025
► pp. 11–34

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Chapter 2
A non-linear Bayesian approach to examine the development of Brazilian Portuguese (L3) vowels by an Argentinean learner

 | Universidade de Brasília
 | Universidade Federal do Rio Grande do Sul
Published online: 11 September 2025
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https://doi.org/10.1075/rmal.14.02lim
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.
Article outline
  • Introduction
  • An introduction to Bayesian Generalized Additive Models
  • Empirical study
    • Global view
    • Focal participant
    • Data collection and analysis procedures
    • Data description
    • Data analysis
    • Modelling vowel development (F1 and F2 values) with GAMMs
    • Modelling acoustic distances with GAMMs
  • Affordances and limitations of Bayesian GAMMs
  • Implications for implementing Bayesian GAMMs in CDST-inspired research
  • Conclusion
  • Notes
  • References
References (24)
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