This may all be correct, but in the end psych delivers a well interpretable output and that should be the essence from the user’s point of view.
The core of my solution (for learning purposes) is this (PCA_Data contains the observations, PCA_HK the estimated number of main components):
PCA_Modell = R"principal($PCA_Daten, $PCA_HK)"
PCA_scores = R"principal($PCA_Daten, $PCA_HK)$scores"
show(PCA_Modell)
As you can see, I use R over RCall. And that is the output:
RObject{VecSxp}
Principal Components Analysis
Call: principal(r = `#JL`$PCA_Daten, nfactors = `#JL`$PCA_HK)
Standardized loadings (pattern matrix) based upon correlation matrix
RC1 RC2 RC3 RC4 h2 u2 com
1 0.91 -0.13 0.07 0.02 0.85 0.15 1.1
2 -0.34 -0.02 -0.72 -0.13 0.64 0.36 1.5
3 0.75 0.04 0.44 0.23 0.81 0.19 1.9
4 0.35 0.46 -0.03 -0.25 0.39 0.61 2.5
5 0.13 0.00 -0.27 0.80 0.73 0.27 1.3
6 -0.14 0.88 0.03 0.07 0.80 0.20 1.1
7 -0.02 0.88 -0.11 0.09 0.79 0.21 1.1
8 0.78 0.10 -0.44 0.01 0.80 0.20 1.6
9 -0.73 0.01 -0.01 -0.25 0.60 0.40 1.2
10 0.15 0.06 0.27 0.76 0.68 0.32 1.4
11 -0.23 -0.11 0.78 -0.13 0.69 0.31 1.3
RC1 RC2 RC3 RC4
SS loadings 2.87 1.80 1.67 1.44
Proportion Var 0.26 0.16 0.15 0.13
Cumulative Var 0.26 0.42 0.58 0.71
Proportion Explained 0.37 0.23 0.21 0.19
Cumulative Proportion 0.37 0.60 0.81 1.00
Mean item complexity = 1.4
Test of the hypothesis that 4 components are sufficient.
The root mean square of the residuals (RMSR) is 0.09
with the empirical chi square 1473.01 with prob < 3.2e-303
Fit based upon off diagonal values = 0.89
The output is easy to read and contains some information on the quality of model estimation. This is basic information for the data analyst.
The value of the latent variables (scores) is also supplied simply (well, Julia (or the function of the package) also supplies this). And by the way, the scree-graphic is delivered as well.
The effort I have to make as a user is quite small. Speaks from my point of view for the R-function. I still see potential for the MultivariateStats package.
Thank you for your support and greetings,
Günter