Question

I’m doing some PCA analysis for my data. and its my first time to try this type of analysis.
I’m having a matrix of a thousand columns and few thousands of rows, and i am trying to make a smaller matrix by getting rid of correlated variables (which are the columns in my case).
everything is going great until the moment, but i am unable to do the next step.
here’s an example to show my data.

         a1    a2    a3    a4    ....    a1000
item1    10    NA     5     3    ....
item2    0.01  0.5    NA   0.07  ....
item3    0.7   0.2    0.8  0.9   ....
                   .
                   .
                   .

I apply the princomp and get the following results

                         Comp.1     Comp.2     Comp.3     Comp.4     ...   Comp.1000
Standard deviation     24.1605431 7.31176669 5.96709553 3.56507807   ...
Proportion of Variance  0.7580933 0.06943108 0.04624186 0.01650621   ...
Cumulative Proportion   0.7580933 0.82752438 0.87376624 0.89027245   ...
                                       .
                                       .
                                       .

Now that i have computed everything…my question is: what command should i use to pick the uncorrelated components and paste them into a new matrix (or simply get rid of the correlated ones)?
how do i specify the range of correlation i want?

Thanks,

Answer 1

I believe you are after the scores. From the help for ?princomp, the resulting object is a list that contains an elements scores:

scores

if scores = TRUE, the scores of the supplied data on the
principal components. These are non-null only if x was supplied, and
if covmat was also supplied if it was a covariance list. For the
formula method, napredict() is applied to handle the treatment of
values omitted by the na.action.

Let’s set up an example (based on example in ?princomp):

summary(pc.cr <- princomp(USArrests, cor = TRUE))
Importance of components:
                          Comp.1    Comp.2    Comp.3     Comp.4
Standard deviation     1.5748783 0.9948694 0.5971291 0.41644938
Proportion of Variance 0.6200604 0.2474413 0.0891408 0.04335752
Cumulative Proportion  0.6200604 0.8675017 0.9566425 1.00000000

You can investigate the result object with str():

str(pc.cr)
List of 7
 $ sdev    : Named num [1:4] 1.575 0.995 0.597 0.416
  ..- attr(*, "names")= chr [1:4] "Comp.1" "Comp.2" "Comp.3" "Comp.4"
 $ loadings: loadings [1:4, 1:4] -0.536 -0.583 -0.278 -0.543 0.418 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:4] "Murder" "Assault" "UrbanPop" "Rape"
  .. ..$ : chr [1:4] "Comp.1" "Comp.2" "Comp.3" "Comp.4"
 $ center  : Named num [1:4] 7.79 170.76 65.54 21.23
  ..- attr(*, "names")= chr [1:4] "Murder" "Assault" "UrbanPop" "Rape"
 $ scale   : Named num [1:4] 4.31 82.5 14.33 9.27
  ..- attr(*, "names")= chr [1:4] "Murder" "Assault" "UrbanPop" "Rape"
 $ n.obs   : int 50
 $ scores  : num [1:50, 1:4] -0.986 -1.95 -1.763 0.141 -2.524 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:50] "Alabama" "Alaska" "Arizona" "Arkansas" ...
  .. ..$ : chr [1:4] "Comp.1" "Comp.2" "Comp.3" "Comp.4"
 $ call    : language princomp(x = USArrests, cor = TRUE)
 - attr(*, "class")= chr "princomp"

Now extract the scores:

head(pc.cr$scores)
               Comp.1     Comp.2      Comp.3       Comp.4
Alabama    -0.9855659  1.1333924 -0.44426879  0.156267145
Alaska     -1.9501378  1.0732133  2.04000333 -0.438583440
Arizona    -1.7631635 -0.7459568  0.05478082 -0.834652924
Arkansas    0.1414203  1.1197968  0.11457369 -0.182810896
California -2.5239801 -1.5429340  0.59855680 -0.341996478
Colorado   -1.5145629 -0.9875551  1.09500699  0.001464887