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Asked: 2026-05-24T03:44:06+00:00

Suppose I ran a factor analysis & got 5 relevant factors. Now, I want

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Suppose I ran a factor analysis & got 5 relevant factors. Now, I want to graphically represent the loading of these factors on the variables. Can anybody please tell me how to do it. I can do using 2 factors. But can’t able to do when number of factors are more than 2.

The 2 factor plotting is given in “Modern Applied Statistics with S”, Fig 11.13. I want to create similar graph but with more than 2 factors. Please find the snap of the Fig mentioned above:
enter image description here

X & y axes are the 2 factors.

Regards,
Ari

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1 Answer

  1. Editorial Team

    Beware: not the answer you are looking for and might be incorrect also, this is my subjective thought.

    I think you run into the problem of sketching several dimensions on a two dimension screen/paper.
    I would say there is no sense in plotting more factors’ or PCs’ loadings, but if you really insist: display the first two (based on eigenvalues) or create only 2 factors. Or you could reduce dimension by other methods also (e.g. MDS).

    Displaying 3 factors’ loadings in a 3 dimensional graph would be just hardly clear, not to think about more factors.

    UPDATE: I had a dream about trying to be more ontopic 🙂

    You could easily show projections of each pairs of factors as @joran pointed out like (I am not dealing with rotation here):

    f <- factanal(mtcars, factors=3)
pairs(f$loadings)

    enter image description here

    This way you could show even more factors and be able to tweak the plot also, e.g.:

    f <- factanal(mtcars, factors=5)
pairs(f$loadings, col=1:ncol(mtcars), upper.panel=NULL, main="Factor loadings")
par(xpd=TRUE) 
legend('topright', bty='n', pch='o', col=1:ncol(mtcars), attr(f$loadings, 'dimnames')[[1]], title="Variables")

    enter image description here

    Of course you could also add rotation vectors also by customizing the lower triangle, or showing it in the upper one and attaching the legend on the right/below etc.

    Or just point the variables on a 3D scatterplot if you have no more than 3 factors:

    library(scatterplot3d)
f <- factanal(mtcars, factors=3)
scatterplot3d(as.data.frame(unclass(f$loadings)), main="3D factor loadings", color=1:ncol(mtcars), pch=20)

    enter image description here

    Note: variable names should not be put on the plots as labels, but might go to a distinct legend in my humble opinion, specially with 3D plots.

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