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Annotate a biplot with Alves direct-reading errors

Source: R/score_axes.R
score_axes.Rd

score_axes() augments the hover information of every mdsDisplay in a bipl5_biplot with the direct-reading diagnostic of Alves (2012). For each observation \(i\) and variable \(j\) the direct-reading error is

Usage

score_axes(x, digits = 2, ...)

# S3 method for bipl5_biplot
score_axes(x, digits = 2, ...)

Arguments

x

A bipl5_biplot produced by scale_mds().

digits

Number of decimal places used when displaying the reading error percentage. Defaults to 2.

...

Currently unused.

Value

A bipl5_biplot whose observation hover tables carry an additional Error column. The object remains fully plottable.

Details

$$\delta_{ij} = \frac{|x_{ij} - \widehat{x}_{ij}|}{s_j},$$

where \(x_{ij}\) is the actual value, \(\widehat{x}_{ij}\) is the value read directly off the calibrated axis for variable \(j\) (i.e. the orthogonal projection of the sample point onto the displayed axis), and \(s_j\) is the scaling constant used when the biplot was drawn. The scaling constant is 1 when the data were not scaled and the column standard deviation \(s_j\) when scale = TRUE was passed to init_biplot(). The quantity is reported in percentage form (\(100\,\delta_{ij}\)) as an extra Error column in the hover table shown when a data point is hovered over.

The diagnostic is computed separately for each mdsDisplay present in the object, because the read-off value \(\widehat{x}_{ij}\) depends on the dimension pair being displayed. The methodology applies uniformly to PCA, PCO and CVA biplots, which all use calibrated linear axes. Spline (non-linear) PCO axes do not admit a single calibrated reading and are left unchanged.

This step is deliberately not performed by default: it is only applied when score_axes() is inserted into the pipeline, e.g.

init_biplot(data) |> scale_mds() |> score_axes() |> plot()

References

Alves, M. R. (2012). Evaluation of the predictive power of biplot axes to automate the construction and layout of biplots based on the accuracy of direct readings from common outputs of multivariate analyses: application to principal component analysis. Journal of Chemometrics, 26(5), 180-190.