In the last decade, Complex Dynamic Systems Theory (CDST) has challenged researchers to try out new methods and techniques. These new approaches have allowed us to rethink the research goals in CDST studies. As a result, not only new means of data collection, but also different statistical procedures, have been employed so as to model language changes in time.
Departing from this scenario, in the last few years we have investigated the development of BP vowels by an Argentinean learner (L2: English; L3: BP) who had been living in Brazil for three years at the beginning of the data collection. We carried out a longitudinal study within a time window of approximately one year and 24 fortnightly data collections in a sentence-reading task. Explicit instruction on BP pronunciation was provided between data collections 10 to 15, aiming to foster more rapid changes in the learner's vowel system.
The acoustic data (F1 and F2 values) from these recordings received different statistical treatments in previous studies, such as Monte-Carlo Analyses (Van Dijk, Verspoor, and Lowie 2011) and Change-Point Analyses (Taylor, 2000). In this study, however, we reanalyzed the data using a Bayesian multilevel regression model, aiming to verify possible advantages of this approach to statistical inference. We highlight, as advantages, the fact that (i) since it is a regression model, all data points (instead of means and standard deviations) are used to inform the model; (ii) since it is Bayesian, the model accounts for the probability of the parameters given the data (instead of the probability of the data given a null-hypothesis), and it incorporates prior knowledge of plausible F1 and F2 values; and (iii) since it is multilevel, both individual- and group-level analyses are easily carried out, thus addressing questions around variability and development within and beyond the individual learner. The fact that Bayesian multilevel regressions are not field-specific, and are proposed to be the default of any probability analysis (McEalreath 2020), is an additional advantage.
The results obtained from this study have important empirical and methodological implications, demonstrating that a general approach to statistical inference can help move CDST applied to second language research beyond its metaphorical interpretation, highlighting several components of Complex Dynamic Systems through the data analysis process.
References
McElreath, R. (2020). Statistical rethinking: A Bayesian course with examples in R and Stan. Chapman and Hall/CRC.
Taylor, W. A. (2000). Change-point analysis: A powerful new tool for detecting changes. Retrieved March 13, 2022, from http://www.variation.com/cpa/tech/changepoint.html.
Van Dijk, M., M. Verspoor & W. Lowie (2011). Variability in second language development from a dynamic systems perspective. In M. Verspoor, K. de Bot & W. Lowie (eds.), A Dynamic Approach to Second Language Development: Methods and Techniques, 55–84. Amsterdam: John Benjamins.
