Abstract
This chapter provides both a theoretical discussion of what multivariate exploratory approaches entail and step-by-step instructions to implement each of them with R. Four methods are presented: correspondence analysis, multiple correspondence analysis, principal component analysis, and exploratory factor analysis. These methods are designed to explore and summarize large and complex data tables by means of summary statistics. They help generate hypotheses by providing informative clusters using the variable values that characterize each observation.
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Notes
- 1.
I am using scare quotes because, as Kilgarriff (2005) puts it, “language is never, ever, ever, random”.
- 2.
See Baayen (2008, Sect. 5.1.1).
- 3.
A second kind of PCA is based on loadings (Baayen 2008, Sect. 5.1.1). Loadings are correlations between the original variables and the unit-scaled principal components. The two kinds of PCA are similar: both are meant to normalize the coordinates of the data points. The variant exemplified in this chapter is more flexible because it allows for the introduction of supplementary variables.
- 4.
- 5.
- 6.
Details on how the data were extracted can be found in this blog post: https://corpling.hypotheses.org/284 (accessed 9 June 2019).
- 7.
- 8.
The code for the extraction was partly contributed by Mathilde Léger, a third-year student at Paris 8 University, as part of her end-of-term project.
- 9.
http://www.natcorp.ox.ac.uk/docs/catRef.xml (accessed 9 June 2019).
- 10.
Several packages and functions implement PCA in R: e.g. princomp( ) and prcomp( ) from the stats package, ggbiplot( ) from the ggbiplot package (which is itself based on ggplot2), dudi.pca( ) from the ade4 package, and PCA( ) from the FactoMineR package. Mind you, princomp( ) and prcomp( ) perform PCA based on loadings.
- 11.
For this kind of analysis, the first two components should represent a cumulative percentage of variance that is far above 50%. The more dimensions there are in the input data table, the harder it will be to reach this percentage.
- 12.
The contribution is a measure of how much an individual contributes to the construction of a component.
- 13.
The squared cosine (cos 2) is a measure of how well an individual is projected onto a component.
- 14.
How many factors are considered worth keeping involves a choice based a metric known as SS loadings, as explained below.
- 15.
The FactoMineR package includes several extensions of factor analysis. Multiple factor analysis (MFA) is used to explore datasets where variables are structured into groups. Like PCA, it can handle continuous and/or categorical variables simultaneously (Pagès 2014). MFA further breaks down into hierarchical multiple factor analysis (Lê and Pagès 2003) and dual multiple factor analysis (Lê and Pagès 2010). Although commonly used in sensorimetrics, these methods are rare in linguistics.
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Desagulier, G. (2020). Multivariate Exploratory Approaches. 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_19
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