Finally, as model interpretation and model criticism with GAMMs require a high level of under-standing of both the method and the theoretical concepts it builds on, it is advisable to engage in a deeper exploration of the issues at hand prior to applying the models in a productive research environment. Here, we provide an overview of key readings, that the analyst may find useful for exploring various types of data and uncovering and adressing effects commonly found in human response data.
First, Wood(2017), a standard reference on GAMs, provides a necessary background in linear models linear mixed models and generalized linear models and introduction to the theory and applications of GAMs, complemented by a wide range of exercises.
In addition to that, we suggest the following articles, which go in depth into the possibilities offered by GAMMs for dealing with various types of language data and uncovering and handling autocorrelation arising from experiment structure. Baayen et al.(2017b) show techniques offered by GAMMs on the analysis of response times in a word naming task, investigation of a pitch contour task in a word naming experiment and a model fitted to the EEG response amplitude to visually
presented compound words. Baayen et al. (2017c) illustrate on three data sets how human factors like learning or fatigue may interact with predictors of interest, both factorial and metric, and demonstrate why fitting maximally complex models is not an advisable strategy, especially within the framework of the generalized additive mixed effects model. Wieling (2018) offers a hands-on tutorial, including the original data and all R commands, for analysing dynamic time series data on the example of articulator trajectories observed using electromagnetic articulography. The paper leads the reader through the steps of data exploration, visualization, modeling of complex interactions and model criticism, introducing a wide variety of techniques and strategies with a detailed and comprehensive rationale for the modeling decisions, offering the reader an opportunity to replicate the analyses and gain more understanding about the material. van Rij et al.(2019) is a tutorial introduction to GAMMs for pupilometry data, illustrating several methods from theitsadug package. Additionally, the extended online documentation of the itsadug package provides prac-tical examples to guide visual inspection of GAMM models (https://cran.r-project.org/web/
packages/itsadug/vignettes/inspect.html), checking for autocorrelation and dealing with it (https://cran.r-project.org/web/packages/itsadug/vignettes/acf.html) and significance testing (https://cran.r-project.org/web/packages/itsadug/vignettes/test.html).
References
Baayen, R. H. and Divjak, D. (2017). Ordinal GAMMs: a new window on human ratings. In Makarova, A., Dickey, S. M., and Divjak, D. S., editors, Thoughts on Language: Studies in Cognitive Linguistics in Honor of Laura A. Janda., pages 39–56. Slavica Publishers, Bloomington, IN.
Baayen, R. H., Tomaschek, F., Gahl, S., and Ramscar, M. (2017a). The Ecclesiastes principle in language change. In Hundt, M., Mollin, S., and Pfenninger, S., editors, The changing English language: Psycholinguistic perspectives, page in press. Cambridge University Press, Cambridge, UK.
Baayen, R. H., van Rij, J., de Cat, C., and Wood, S. N. (2017b). Autocorrelated errors in ex-perimental data in the language sciences: Some solutions offered by generalized additive mixed models. In Speelman, D., Heylen, K., and Geeraerts, D., editors,Mixed Effects Regression Models in Linguistics, page to appear. Springer, Berlin.
Baayen, R. H., Vasishth, S., Bates, D., and Kliegl, R. (2017c). The cave of shadows. Addressing the human factor with generalized additive mixed models. Journal of Memory and Language, 94:206–234.
Box, G. E. P. (1976). Science and statistics. Journal of the American Statistical Association, 71:791–799.
Davies, M. (2010). The Corpus of Historical American English (COHA): 400+ million words, 1810–2009.
Divjak, D. (2016). The role of lexical frequency in the acceptability of syntactic variants: Evidence from that-clauses in Polish. Cognitive Science, DOI:10.1111/cogs.12335:1–29.
Divjak, D., Milin, P., and Baayen, R. H. (2017). A learning perspective on individual differences in skilled reading: Exploring and exploiting orthographic and semantic discrimination cues.Journal of Experimental Psychology: Learning, Memory and Cognition, 43(11):1730–1751.
Elleg˚ard, A. (1953). The auxiliary do: The establishment and regulation of its use in English.
Almquist & Wiksell, Stockholm.
Hastie, T. and Tibshirani, R. (1990). Generalized Additive Models. Chapman & Hall, London.
Johnson, K. (2004). Massive reduction in conversational American English. InSpontaneous speech:
data and analysis. Proceedings of the 1st session of the 10th international symposium, pages 29–54, Tokyo, Japan. The National International Institute for Japanese Language.
Linke, M., Broeker, F., Ramscar, M., and Baayen, R. H. (2017). Are baboons learning “ortho-graphic” representations? probably not. PLOS-ONE, 12(8):e0183876.
Marra, G. and Wood, S. N. (2012). Coverage properties of confidence intervals for generalized additive model components. Scandinavian Journal of Statistics, 39:53–74.
Milin, P., Feldman, L. B., Ramscar, M., Hendrix, P., and Baayen, R. H. (2017). Discrimination in lexical decision. PLOS-one, 12(2):e0171935.
Nychka, D. (1988). Bayesian confidence intervals for smoothing splines. Journal of the American Statistical Association, 83:1134–1143.
Pitt, M., Johnson, K., Hume, E., Kiesling, S., and Raymond, W. (2005). The Buckeye corpus of conversational speech: labeling conventions and a test of transcriber reliability. Speech Commu-nication, 45(1):89–95.
Tomaschek, F., Tucker, B., and Baayen, R. H. (2018). Practice makes perfect: The consequences of lexical proficiency for articulation. Linguistic Vanguard, page to appear.
Tucker, B. V., Sims, M., and Baayen, R. H. (2018). Opposing forces on acoustic duration. Manu-script, University of Alberta and University of T¨ubingen.
van Rij, J., Hendriks, P., van Rijn, H., Baayen, R. H., and Wood, S. N. (2019). Analyzing the time course of pupillometric data. Trends in hearing, 23:2331216519832483.
van Rij, J., Wieling, M., Baayen, R. H., and van Rijn, H. (2017). itsadug: Interpreting time series and autocorrelated data using GAMMs. R package version 2.3.
Wieling, M. (2018). Analyzing dynamic phonetic data using generalized additive mixed modeling:
A tutorial focusing on articulatory differences between L1 and L2 speakers of English. Journal of Phonetics, 70:86–116.
Wieling, M., Montemagni, S., Nerbonne, J., and Baayen, R. H. (2014). Lexical differences between Tuscan dialects and standard Italian: Accounting for geographic and socio-demographic variation using generalized additive mixed modeling. Language, 90(3):669–692.
Wieling, M., Nerbonne, J., and Baayen, R. H. (2011). Quantitative social dialectology: Explaining linguistic variation geographically and socially. PLoS ONE, 6(9):e23613.
Wieling, M., Tomaschek, F., Arnold, D., Tiede, M., Br¨oker, F., Thiele, S., Wood, S. N., and Baayen, R. H. (2016). Investigating dialectal differences using articulography. Journal of Phonetics, 59:122–143.
Wood, S. N. (2006). Generalized Additive Models. Chapman & Hall/CRC, New York.
Wood, S. N. (2013a). On p-values for smooth components of an extended generalized additive model. Biometrika, 100:221–228.
Wood, S. N. (2013b). A simple test for random effects in regression models. Biometrika, 100:1005–
1010.
Wood, S. N. (2017). Generalized Additive Models. Chapman & Hall/CRC, New York.