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Modern Psychometrics with R pp 289–311Cite as

Biplots

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Abstract

Biplots are a multivariate scatterplot concept to visualize row and column structures in complex data. It can be applied to any of the exploratory methods presented in previous chapters. We introduce biplots by means of a multivariate regression with two predictors. Subsequently, this concept is applied to principal component analysis, where biplots are one of the classical output visualization techniques. The same plotting principle is adopted to Princals. In the following section, biplots for multidimensional scaling are introduced where external covariates are mapped onto the configuration. Finally, biplots within a correspondence analysis context are discussed where they are simply asymmetric maps.

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Notes

  1. 1.

    \(\|\mathbf x\| = \sqrt {\sum _i x_i^2}\)

  2. 2.

    The inner product is 〈x, y〉 =∑i x i y i.

  3. 3.

    Note that we use Λ instead of D as in Sect. 6.1.1, in order to be consistent with the settings in R’s biplot function.

  4. 4.

    For our purposes it is sufficient to know that the Mahalanobis distance is similar to the Euclidean distance, but it incorporates weights in terms of the variance-covariance matrix (see, e.g., Joliffe, 2002, for details).

  5. 5.

    Thanks to Christine Hooker for sharing this dataset.

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Authors and Affiliations

  1. Department of Psychology, Harvard University, Cambridge, MA, USA

    Patrick Mair

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  1. Patrick Mair
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Mair, P. (2018). Biplots. In: Modern Psychometrics with R. Use R!. Springer, Cham. https://doi.org/10.1007/978-3-319-93177-7_10

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