Abstract
This chapter presents fixed-effects regression modeling as a family of methods that describe a dependent variable in terms of one or more independent variables. The chapter focuses on multiple linear regression and on binomial logistic regression, discussing examples of regression analyses on the basis of corpus-linguistic data. The chapter offers descriptions of published studies that have used these methods. Besides explaining the fundamental notions and assumptions of different types of regression, the chapter also illustrates practical aspects of applying regression analyses through the use of artificially created data sets. In order to give readers a practical introduction to regression modeling, it is shown how manipulations of the underlying data result in different outcomes of the respective analyses. The chapter further discusses how the results of regression analyses can be usefully visualized. A selection of resources for further reading is included to offer readers a starting point for further study of regression modeling.
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Notes
- 1.
See Gries (2013:28) for a general discussion of p-values.
- 2.
This is just but one possible regression model for binary outcomes (Agresti and Kateri 2011). Furthermore, it might appear as a bit arbitrary that the response variable is the log odds-ratio rather than a more “intuitive” measure (like the arithmetic difference of probabilities or so.) The reason is that this particular model can be analyzed (and computationally treated) within the framework of generalized linear models (Gelman and Hill 2006).
- 3.
If there is a natural ordering of the response variable (e.g. we assume that excellent > perfect > great in terms of their valency) then ordinal regression might be a more informative tool (Harrell 2015).
- 4.
We acknowledge that the artificially created data set suffers from overdispersion, i.e. the variation is higher than statistically expected. We do not discuss this problem or its consequences here, as that would go beyond the intended scope of the chapter.
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Further Reading
Further Reading
Baayen, R.H. 2008. Analyzing Linguistic Data: A Practical Introduction to Statistics . Cambridge University Press, Cambridge.
Baayen’s introduction to statistics for linguistics is a cornerstone reference that not only covers the regression techniques that were discussed in this chapter, but also offers a more thorough discussion of nonlinear predictors, model criticism and validation, as well as regression with breakpoints.
Gries, S.T. 2013. Statistics for Linguistics with R: A Practical Introduction . Second edition. De Gruyter, Berlin.
Gries’s book includes several chapters on regression techniques that are illustrated with concrete data sets. The chapters gradually build up in complexity, presenting analyses with binary, categorical, and numerical predictors. The chapters further offer insights into ordinal, multinomial, and Poisson regression.
Levshina, N. 2015. How to do Linguistics with R: Data exploration and statistical analysis . John Benjamins, Amsterdam.
Levshina’s book offers a particularly learner-friendly discussion of regression techniques. The book presents these methods as ways of approaching linguistic questions, and it places emphasis on data visualization. The examples that are covered include an application of logistic regression to the choice between the Dutch causative constructions with doen and laten.
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Hilpert, M., Blasi, D.E. (2020). Fixed-Effects Regression Modeling. In: Paquot, M., Gries, S.T. (eds) A Practical Handbook of Corpus Linguistics. Springer, Cham. https://doi.org/10.1007/978-3-030-46216-1_21
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