biplot scaling options (ggbiplot)

Question

[Lucy]

Hi,

I have a prcomp object (generated using the prcomp function) and I am trying to generate a biplot using ggbiplot, however I am confused about the different scaling options and their impact on the meaning of the plot.

ggbiplot(pcobj, choices = 1:2, scale = 1, pc.biplot = TRUE, obs.scale = 1 - scale, var.scale = scale)

scale = covariance biplot (scale = 1), form biplot (scale = 0). When scale = 1, the inner product between the variables approximates the covariance and the distance between the points approximates the Mahalanobis distance.

obs.scale = scale factor to apply to observations

var.scale = scale factor to apply to variables

I am not sure which of these scaling options I should choose for a prcomp object? I have seen lots of people set obs.scale = 1 and var.scale = 1, but I don't understand the reason for this.

What does the line length and angle actually correspond to in a biplot? I get the general idea that a high value on PC1 indicates that the variable has a strong influence on PC1 whilst a small value indicates a small influence. And that if the arrow is pointing to the right, then that variable has a positive impact on the PC.

Thanks for the help!!

Best wishes,

Lucy

[Lucy]

Thank you for suggesting PCAtools - I will try this out.

Why do you set obs.scale and var.scale to 1 in the command above? If you change obs.scale, it seems to modify the PC1 axis, while changing var.scale modifies the loading arrows.

[Kevin Blighe]

If you are unsure what are the roles of these parameters, then I would leave them at the default, or use some other PCA function that has actually passed review by a third party. ggbiplot is on neither CRAN nor BioConductor, the main R package repositories, and is therefore simply some code posted to GitHub. As I mentioned, in addition, the project seems abandoned, with the last commit >4 years ago

The actual lengths of those arrows means nothing, as far as I am aware.

Answer 1

[Kevin Blighe]

I think that this function is still in development, or was abandoned (last commit was in 2015). Implementation of the scale parameter has no apparent effect:

library(ggbiplot)
data(wine)
wine.pca <- prcomp(wine, scale. = TRUE)

g1 <- ggbiplot(wine.pca, scale = 1, obs.scale = 1, var.scale = 1,
  groups = wine.class, ellipse = TRUE, circle = TRUE) +
  scale_color_discrete(name = '') +
  theme(legend.direction = 'horizontal', legend.position = 'top')


g2 <- ggbiplot(wine.pca, scale = 0, obs.scale = 1, var.scale = 1,
  groups = wine.class, ellipse = TRUE, circle = TRUE) +
  scale_color_discrete(name = '') +
  theme(legend.direction = 'horizontal', legend.position = 'top')


cowplot::plot_grid(g1, g2, ncol = 2)

Without spending too much time trying to understand why the function is applying these extra calculations, I would point you to PCAtools (by Aaron and I), which is on Bioconductor. With PCAtools, your input is just a data-matrix and it will produce the same output as prcomp().

Kevin

[Lucy]

Ok thank you for the advice.