Building scores from princomp loads in R

Question

I would like to be able to build estimates of the analysis of the main components using its downloads, but I cannot understand what the princomp function does when it calculates the estimates of the dataset. Toy example:

cc <- matrix(1:24,ncol=4) PCAcc <- princomp(cc,scores=T,cor=T) PCAcc$loadings Loadings: Comp.1 Comp.2 Comp.3 Comp.4 [1,] 0.500 0.866 [2,] 0.500 -0.289 0.816 [3,] 0.500 -0.289 -0.408 -0.707 [4,] 0.500 -0.289 -0.408 0.707 PCAcc$scores Comp.1 Comp.2 Comp.3 Comp.4 [1,] -2.92770 -6.661338e-16 -3.330669e-16 0 [2,] -1.75662 -4.440892e-16 -2.220446e-16 0 [3,] -0.58554 -1.110223e-16 -6.938894e-17 0 [4,] 0.58554 1.110223e-16 6.938894e-17 0 [5,] 1.75662 4.440892e-16 2.220446e-16 0 [6,] 2.92770 6.661338e-16 3.330669e-16 0 

I understand that scores are a linear combination of loads and scaled input data. Hand Try:

 rescaled <- t(t(cc)-apply(cc,2,mean)) rescaled%*%PCAcc$loadings Comp.1 Comp.2 Comp.3 Comp.4 [1,] -5 -1.332268e-15 -4.440892e-16 0 [2,] -3 -6.661338e-16 -3.330669e-16 0 [3,] -1 -2.220446e-16 -1.110223e-16 0 [4,] 1 2.220446e-16 1.110223e-16 0 [5,] 3 6.661338e-16 3.330669e-16 0 [6,] 5 1.332268e-15 4.440892e-16 0 

Columns are disabled at 1.707825, 2, and 1.3333333, respectively. Why is this? Since the matrix of these toys has the same variance in each column, normalization is not needed here. Any help is appreciated.

Thanks!

Answer 1

You need

 scale(cc,PCAcc$center,PCAcc$scale)%*%PCAcc$loadings 

or easier

 predict(PCAcc,newdata=cc)