PCR after PCA with mixed data - how to extract/export the PCs as new variables in R?

Question

As the title/question implies I ran a PCA with mixed data, i.e. categorical and numeric, in R, once with the "FactoMineR" and "factoextra" packages (analysis version 1) and once with the "PCAmixdata" package (analysis version 2) (just to compare both approaches, out of curiosity).

The original dataset consists of 184 variables/953 samples and the idea behind the PCA was to reduce the dimensionality of the dataset in order to gain less but more informative components (variables). This all worked and after both analysis versions it seems that the first 5 components/dimension are sound (largest eigenvalues and visual inspection of the scree plot). Now I would like to use these 5 PCs as predictor variables in a subsequent (principal component) regression. And this is where I'm stuck. I don't know how to extract/export the PCs into new predictor variables so that each of the 953 subjects has a value in each of the 5 dimensions; I don't know which part of the output holds the information I need, or if further manual calculations will be necessary before I can extract the PC variables. If so, I wouldn't know the formula.

FYI: The output for both analysis versions produces eigenvalues of the dimensions, "coordinates", "Cos2" (-> quality of representation of a variable through a PC) and "contributions" (-> contributions (in percentage) of the variables to the principal components) for both the variables and individuals (samples). With the "PCAmixdata" package (analysis version 2) one can also examine the "squared loadings" and the "coefficents of the linear combinations defining the PC" for the variables only.

I am aware of the pcr() function of the "pls" package but it doesn't seem to work since it inherently performs a PCA first and regular PCAs - to my knowledge - cannot use categorical data.

Thank you for your answers in advance!

Answer 1

They are almost similar, if you run a pca using FactoMineR, you need the principal component score and they are stored under $svd$U because FactoMineR performs a pca using svd (you can see how they are related).

So for example using mtcars:

library(FactoMineR)
mpg = mtcars[,"mpg"]
pca.res = PCA(mtcars[,-1],graph=FALSE)

To get back the so called principal component scores, normally used in prcomp etc you do:

PCs = pca.res$svd$u %*% diag(pca.res$svd$d)

Because this is essentially multiplying the U matrix by its corresponding eigen value, for a regression this is not quite essential. However for complete sake, we can do:

PCs = PCs[,1:5]

Or you can do:

PCs = pca.res$ind$coord[,1:5]

followed by:

fit_PCs = lm(mpg ~ PCs)

If you use pcr() from pls:

fit_pls = pcr(mpg ~ .,data=mtcars,ncomp=5,
validation="none",scale=TRUE,center=TRUE)

The fitted values for 5 components are in:

fitted(fit_pls)[,,5]

So we check the fitted values from both:

plot(fitted(fit_pls)[,,5],fitted(fit_PCs),xlab="pls_5comp",ylab="PCA+lm")