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29 - Statistical Modeling in L3/Ln Acquisition

from Part VI - Research Methods in L3/Ln

Published online by Cambridge University Press:  13 July 2023

Jennifer Cabrelli
Affiliation:
University of Illinois, Chicago
Adel Chaouch-Orozco
Affiliation:
The Hong Kong Polytechnic University
Jorge González Alonso
Affiliation:
Universidad Nebrija, Spain and UiT, Arctic University of Norway
Sergio Miguel Pereira Soares
Affiliation:
Max Planck Institute for Psycholinguistics
Eloi Puig-Mayenco
Affiliation:
King's College London
Jason Rothman
Affiliation:
UiT, Arctic University of Norway and Universidad Nebrija, Spain
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Summary

This chapter introduces Bayesian data analysis and shows how such an approach can better deal with the intricacies of Ln acquisition data. The data analyzed is simulated based on Rothman’s (2010) study to demonstrate how we can use Bayesian models to estimate variables of interest in R. The chapter discusses (1) how to tackle smaller sample sizes and (2) how to incorporate theoretical principles and assumptions into our statistical analysis. As will be shown, in addition to its general advantages, Bayesian data analysis provides an effective toolset to address both (1) and (2). It also offers a much more nuanced and comprehensive approach to meet the methodological needs in the field.

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Publisher: Cambridge University Press
Print publication year: 2023

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References

Akaike, H. (1974). A New Look at the Statistical Model Identification. Automatic Control, IEEE Transactions on, 19(6), 716723.Google Scholar
Amrhein, V., Greenland, S., & McShane, B. (2019). Scientists Rise Up against Statistical Significance. Nature, 567, 305307.Google Scholar
Bayes, T. (1763). LII. An Essay towards Solving a Problem in the Doctrine of Chances. By the Late Rev. Mr. Bayes, FRS Communicated by Mr. Price, in a Letter to John Canton, AMFR S. Philosophical Transactions of the Royal Society of London, 370418.Google Scholar
Bürkner, P. C. (2016). “brms”: Bayesian Regression Models Using Stan. R package version 1.5.0.Google Scholar
Cabrelli, J., & Pichan, C. (2021). Initial Phonological Transfer in L3 Brazilian Portuguese and Italian. Linguistic Approaches to Bilingualism, 11(2), 131167.CrossRefGoogle Scholar
Cabrelli Amaro, J., Flynn, S., & Rothman, J. (2012). Third Language Acquisition in Adulthood. Amsterdam: John Benjamins.CrossRefGoogle Scholar
Carpenter, B., Gelman, A., Homan, M., et al. (2017). Stan: A Probabilistic Programming Language. Journal of Statistical Software, Articles, 76(1), 132.Google Scholar
Carreiras, M., & Clifton, C. (1993). Relative Clause Interpretation Preferences in Spanish and English. Language and Speech, 36(4), 353372.Google Scholar
Carreiras, M., & Clifton, C. (1999). Another Word on Parsing Relative Clauses: Eyetracking Evidence from Spanish and English. Memory & Cognition, 27(5), 826833.CrossRefGoogle ScholarPubMed
Dussias, P. E. (2004). Parsing a First Language Like a Second: The Erosion of L1 Parsing Strategies in Spanish–English Bilinguals. International Journal of Bilingualism, 8(3), 355371.Google Scholar
Fernandez, E. M. (2002). Relative Clause Attachment in Bilinguals and Monolinguals. Advances in Psychology, 134, 187215.Google Scholar
Flynn, S., Foley, C., & Vinnitskaya, I. (2004). The Cumulative-Enhancement Model for Language Acquisition: Comparing Adults’ and Children’s Patterns of Development in First, Second and Third Language Acquisition of Relative Clauses. International Journal of Multilingualism, 1(1), 316.Google Scholar
Fodor, J. D. (2002). Prosodic Disambiguation in Silent Reading. In Hirotani, M (Ed.), Proceedings of the 32nd Annual Meeting of the North East Linguistic Society. Amherst, MA: GLSA Publications.Google Scholar
Garcia, G. D. (2020). Language Transfer and Positional Bias in English Stress. Second Language Research, 36(4), 445474.Google Scholar
Garcia, G. D. (2021). Data Visualization and Analysis in Second Language Research. New York: Routledge.Google Scholar
Gelman, A. (2008). Objections to Bayesian Statistics. Bayesian Analysis, 3(3), 445449.CrossRefGoogle Scholar
Gelman, A., & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. New York: Cambridge University Press.Google Scholar
Gelman, A., & Su, Y.-S. (2021). arm: Data Analysis Using Regression and Multilevel/Hierarchical Models. R package version 1.12–2.Google Scholar
Gelman, A., Carlin, J. B., Stern, H. S., et al. (2014). Bayesian Data Analysis (3rd ed.; vol. 2). Boca Raton: Chapman & Hall/CRC.Google Scholar
Gibson, E., & Pearlmutter, N. J. (1998). Constraints on Sentence Comprehension. Trends in Cognitive Sciences, 2(7), 262268.Google Scholar
Gibson, E., Pearlmutter, N., Canseco-Gonzalez, E., & Hickok, G. (1996). Recency Preference in the Human Sentence Processing Mechanism. Cognition, 59(1), 2359.CrossRefGoogle ScholarPubMed
Harrell, Jr., & Frank, E. (2021). Hmisc: Harrell Miscellaneous. R package version 4.6–0.Google Scholar
Hox, J., & McNeish, D. (2020). Small Samples in Multilevel Modeling. In van De Schoot, R., & Miočević, M. (Eds.), Small Sample Size Solutions: A Guide for Applied Researchers and Practitioners. New York: Routledge.Google Scholar
Kruschke, J. K. (2013). Bayesian Estimation Supersedes the t Test. Journal of Experimental Psychology: General, 142(2), 573603.Google Scholar
Kruschke, J. K. (2015). Doing Bayesian Data Analysis: A Tutorial with R, JAGS, and Stan (2nd ed.). London: Academic Press.Google Scholar
Kruschke, J. K. (2021). Bayesian Analysis Reporting Guidelines. Nature Human Behaviour, 5(10), 12821291.Google Scholar
Kruschke, J. K, Aguinis, H., & Joo, H. (2012). The Time Has Come: Bayesian Methods for Data Analysis in the Organizational Sciences. Organizational Research Methods, 15(4), 722752.Google Scholar
Lamprecht, A.-L., Garcia, L., Kuzak, M., et al. (2020). Towards FAIR Principles for Research Software. Data Science, 3(1), 3759.Google Scholar
McElreath, R. (2020). Statistical Rethinking: A Bayesian Course with Examples in R and Stan (2nd ed.). Boca Raton: Chapman & Hall/CRC.CrossRefGoogle Scholar
McGrayne, S. B. (2011). The Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines, & Emerged Triumphant from Two Centuries of Controversy. New Haven: Yale University Press.Google Scholar
McNeish, D. (2016). On Using Bayesian Methods to Address Small Sample Problems. Structural Equation Modeling: A Multidisciplinary Journal, 23(5), 750773.Google Scholar
Miyamoto, E. T. (1998). Relative Clause Attachment in Brazilian Portuguese. Unpublished manuscript. Massachusetts Institute of Technology.Google Scholar
Nicenboim, B., Schad, D. J., & Vasishth, S. (2021). An Introduction to Bayesian Data Analysis for Cognitive Science. https://vasishth.github.io/bayescogsci/book/.Google Scholar
Nuzzo, R. (2014). Scientific Method: Statistical Errors. Nature News, 506(7487), 150152.CrossRefGoogle ScholarPubMed
Plonsky, L. (2013). Study Quality in SLA: An Assessment of Designs, Analyses, and Reporting Practices in Quantitative L2 Research. Studies in Second Language Acquisition, 35(4), 655687.Google Scholar
Plonsky, L. (2014). Study Quality in Quantitative L2 Research (1990–2010): A Methodological Synthesis and Call for Reform. The Modern Language Journal, 98(1), 450470.Google Scholar
R Core Team. (2021). R: A Language and Environment for Statistical Computing. Vienna: R Foundation for Statistical Computing.Google Scholar
Rothman, J. (2010). On the Typological Economy of Syntactic Transfer: Word Order and Relative Clause High/Low Attachment Preference in L3 Brazilian Portuguese. International Review of Applied Linguistics in Teaching (IRAL), 48(2–3), 245273.Google Scholar
Rothman, J. (2011). L3 Syntactic Transfer Selectivity and Typological Determinacy: The Typological Primacy Model. Second Language Research, 27(1), 107127.Google Scholar
RStudio Team. (2021). RStudio: Integrated Development Environment for R. Boston, MA: RStudio, PBC.Google Scholar
Sanz, C., & Lado, B. (2008). Third Language Acquisition Research Methods. Boston, MA: Springer US.Google Scholar
Sorensen, T., Hohenstein, S., & Vasishth, S. (2016). Bayesian Linear Mixed Models Using Stan: A Tutorial for Psychologists, Linguists, and Cognitive Scientists. The Quantitative Methods for Psychology, 12(3), 175200.Google Scholar
Van De Schoot, R., Broere, J. J, Perryck, K. H, et al. (2015). Analyzing Small Data Sets Using Bayesian Estimation: The Case of Posttraumatic Stress Symptoms Following Mechanical Ventilation in Burn Survivors. European Journal of Psychotraumatology, 6(1), article 25216.Google Scholar
Vasishth, S., Nicenboim, B., Beckman, M. E, Li, F., & Kong, E. J. (2018). Bayesian Data Analysis in the Phonetic Sciences: A Tutorial Introduction. Journal of Phonetics, 71, 147161.Google Scholar
Vehtari, A., Gelman, A., & Gabry, J. (2017). Practical Bayesian Model Evaluation Using Leave-One-Out Cross-Validation and WAIC. Statistics and Computing, 27(5), 14131432.Google Scholar
Watanabe, S. (2013). A Widely Applicable Bayesian Information Criterion. Journal of Machine Learning Research, 14, 867897.Google Scholar

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