I am searching for an explanation what the x and y axis within a PCA analysis really means? I could not find any explanation on this topic, can somebody help me with it?
So, just as an example (output of the psych
R-package, available on CRAN):
Principal Components Analysis
Call: principal(r = Thurstone, nfactors = 3, rotate = "Promax", n.obs = 213) Standardized loadings (pattern matrix) based upon correlation matrix
PC1 PC2 PC3 h2 u2 com
Sentences 0.92 0.01 0.01 0.86 0.14 1.0
Vocabulary 0.90 0.10 -0.05 0.86 0.14 1.0
Sent.Completion 0.91 0.04 -0.04 0.83 0.17 1.0
First.Letters 0.01 0.84 0.07 0.78 0.22 1.0
4.Letter.Words -0.05 0.81 0.17 0.75 0.25 1.1
Suffixes
Letter.Series
Pedigrees
Letter.Group
0.18 0.79 -0.15 0.70 0.30 1.2
0.03 -0.03 0.88 0.78 0.22 1.0
0.45 -0.16 0.57 0.67 0.33 2.1
-0.19 0.19 0.86 0.75 0.25 1.2
PC1 PC2 PC3
2.83 2.19 1.96
0.31 0.24 0.22
0.31 0.56 0.78
SS loadings
Proportion Var
Cumulative Var
Proportion Explained 0.41 0.31 0.28
Cumulative Proportion 0.41 0.72 1.00
With component correlations of
PC1 PC2 PC3
PC1 1.00 0.51 0.53
PC2 0.51 1.00 0.44
PC3 0.53 0.44 1.00
Mean item complexity = 1.2
Test of the hypothesis that 3 components are sufficient.
The root mean square of the residuals (RMSR) is 0.06
with the empirical chi square 56.17 with prob < 1.1e-07
Fit based upon off diagonal values = 0.98
So, if I plot this, we have the Sentences
at 0.92 on the X axis and at 0.01 on the Y axis (I skipped the 3rd dimension).
What would a value of 1 or 0.5 actually mean?
promax
rotation and this is not what I did. I used the standard setting (varimax
) which might also be complicated but I thought I might be on the save side... I actually only wonder, why some PCA axis range further then 1 and I really try to understand, what those dimensions are. $\endgroup$