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I am new to R, and am working on a problem of *mporting and working with correlation matrix as the only data source in PCA and PCF in R

I have referred to stack overflow answer banks and even books, I could not find any hints, it make it like R only work with variables data file whereas in SAS you can simply input the correlation matrix and get the PCA and PCF result easily. Hope I am wrong.

I tried to look at stack overflow answer banks, and they are mostly about how to calculate the cor matrix or eigenvalue decomposition.

Below is my attempts:

setwd("D:/BlueHDD/MAQAB/RStudio/R/PCA/Intelligence")

mydata <- read.csv("Intelligence.csv",na.strings = ".")

head(mydata)

 X M P C E H F
1 M 1.000 0.620 0.540 0.320 0.284 0.370
2 P 0.620 1.000 0.510 0.380 0.351 0.430
3 C 0.540 0.510 1.000 0.360 0.336 0.405
4 E 0.320 0.380 0.360 1.000 0.686 0.730
5 H 0.284 0.351 0.336 0.686 1.000 0.735
6 F 0.370 0.430 0.405 0.730 0.735 1.000

ii <- as.matrix(mydata[,2:7])

rownames(ii)<- c ("M","P","C","E","H","F")

colnames(ii)<- c ("M","P","C","E","H","F")

head(ii)

 M P C E H F
M 1.000 0.620 0.540 0.320 0.284 0.370
P 0.620 1.000 0.510 0.380 0.351 0.430
C 0.540 0.510 1.000 0.360 0.336 0.405
E 0.320 0.380 0.360 1.000 0.686 0.730
H 0.284 0.351 0.336 0.686 1.000 0.735
F 0.370 0.430 0.405 0.730 0.735 1.000

myPCA <- eigen(ii)

head(myPCA)

$values

[1] 3.3670861 1.1941791 0.5070061 0.3718472 0.3131559 0.2467257

$vectors

 [,1] [,2] [,3] [,4] [,5] [,6]
[1,] -0.3677678 -0.5098401 0.266985551 0.72768020 0.047584025 -0.04178482
[2,] -0.3913477 -0.4092063 0.485916591 -0.66464527 -0.005392018 -0.03872816
[3,] -0.3719504 -0.3825819 -0.831626240 -0.15204371 -0.003331423 -0.02352388
[4,] -0.4321872 0.3748248 0.021531885 0.06531777 -0.742970281 -0.34056682
[5,] -0.4219572 0.4214599 0.002730054 0.01174474 0.665109730 -0.44922966
[6,] -0.4565228 0.3288196 0.023032686 0.03473540 0.057617669 0.82365511

myPCA$values

[1] 3.3670861 1.1941791 0.5070061 0.3718472 0.3131559 0.2467257

myPCA$vectors

 [,1] [,2] [,3] [,4] [,5] [,6]
[1,] -0.3677678 -0.5098401 0.266985551 0.72768020 0.047584025 -0.04178482
[2,] -0.3913477 -0.4092063 0.485916591 -0.66464527 -0.005392018 -0.03872816
[3,] -0.3719504 -0.3825819 -0.831626240 -0.15204371 -0.003331423 -0.02352388
[4,] -0.4321872 0.3748248 0.021531885 0.06531777 -0.742970281 -0.34056682
[5,] -0.4219572 0.4214599 0.002730054 0.01174474 0.665109730 -0.44922966
[6,] -0.4565228 0.3288196 0.023032686 0.03473540 0.057617669 0.82365511

The problem now in the vector, all the "+" and "-" are opposite !

Also, from here, I don't know how to get the loading matrix. I tried the below but fails:

fit <- princomp(ii)

summary(fit) # print variance accounted for 

loadings(fit) # pc loadings 

plot(fit,type="lines") # scree plot 

fit$scores # the principal components

biplot(fit)

You can perform PCA in R with the princomp function. The documentation says that if you supply the argument covmat it will compute the principal components from the covariance matrix. But it also works to use this argument with the correlation matrix.

Here is a simple example using the iris data.

## principal components from the original data
princomp(iris[,1:4], cor=T)
Standard deviations:
 Comp.1 Comp.2 Comp.3 Comp.4 
1.7083611 0.9560494 0.3830886 0.1439265

Now suppose that you only have a correlation matrix

## from correlation matrix
CM = cor(iris[,1:4])
myPCA = princomp(covmat=CM)
myPCA
Standard deviations:
 Comp.1 Comp.2 Comp.3 Comp.4 
1.7083611 0.9560494 0.3830886 0.1439265 

You get the same answer either way. If you want the loadings, they are stored in the myPCA structure.

myPCA$loadings

Loadings:
 Comp.1 Comp.2 Comp.3 Comp.4
Sepal.Length 0.521 0.377 0.720 0.261
Sepal.Width -0.269 0.923 -0.244 -0.124
Petal.Length 0.580 -0.142 -0.801
Petal.Width 0.565 -0.634 0.524

 Comp.1 Comp.2 Comp.3 Comp.4
SS loadings 1.00 1.00 1.00 1.00
Proportion Var 0.25 0.25 0.25 0.25
Cumulative Var 0.25 0.50 0.75 1.00