how to get Proportion Explained, RMSR and chi-squared?

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Assessment

Difficulty
4/5
Estimated time
3-5 days
Newbie friendliness
35/100
Issue type
Feature
Clarity
Mostly clear
Activity status
Stale
Tech stack
python
Domain
data

Research direction

Start at the FactorAnalyzer(n_factors=3, rotation="varimax", method="principal") entry point and compare its existing SS loadings, Proportion Var, and Cumulative Var results with the supplied R output. Review how the library exposes fit statistics, then determine what is needed for Proportion Explained, RMSR, chi-squared, and the sufficiency hypothesis; done means these values are available and agree with the example.

Written by the indexing model from the issue text.

Description

Is your feature request related to a problem? Please describe.
Dataset:

ifanmot.csv

R code:

fan <- principal(ifanmot[,1:42],nfactors=3,rotate="varimax")
print(fan,cut=.5,sort=TRUE)

R output:

Principal Components Analysis
Call: principal(r = ifanmot[, 1:42], nfactors = 3, rotate = "varimax")
Standardized loadings (pattern matrix) based upon correlation matrix

                       RC1  RC2  RC3
SS loadings           9.63 5.53 4.96
Proportion Var        0.23 0.13 0.12
Cumulative Var        0.23 0.36 0.48
Proportion Explained  0.48 0.27 0.25
Cumulative Proportion 0.48 0.75 1.00

Mean item complexity =  1.7
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  2531.01  with prob <  1.2e-194 

Fit based upon off diagonal values = 0.97

Describe the solution you'd like
Using FactorAnalyzer(n_factors=3, rotation="varimax", method="principal") in Python I know how to get SS loadings, Proportion Var, and Cumulative Var and I get the same values as with R.

I do not know how to get Proportion Explained (and Cumulative Proportion would be nice, although I can compute that). Proportion Explained would be very useful to assess the performance of the PCA. But I can't get it from the Python library.

Same question for the hypothesis that 3 components are sufficient, and the RMSR and chi-squared.

Dominant language
Python
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