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A Factor Analysis class

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This is a Python module to perform exploratory factor analysis, with optional varimax and promax rotations. Estimation can be performed using a minimum residual (minres) solution, or maximum likelihood estimation (MLE).

Portions of this code are ported from the excellent R library psych.

Please see the official documentation for additional details.


Exploratory factor analysis (EFA) is a statistical technique used to identify latent relationships among sets of observed variables in a dataset. In particular, EFA seeks to model a large set of observed variables as linear combinations of some smaller set of unobserved, latent factors.

The matrix of weights, or factor loadings, generated from an EFA model describes the underlying relationships between each variable and the latent factors. Typically, a number of factors (K) is selected such that it is substantially smaller than the number of variables. The factor analysis model can be estimated using a variety of standard estimation methods, including but not limited to OLS, minres, or MLE.

Factor loadings are similar to standardized regression coefficients, and variables with higher loadings on a particular factor can be interpreted as explaining a larger proportion of the variation in that factor. In many cases, factor loading matrices are rotated after the factor analysis model is estimated in order to produce a simpler, more interpretable structure to identify which variables are loading on a particular factor.

Two common types of rotations are:

  1. The varimax rotation, which rotates the factor loading matrix so as to maximize the sum of the variance of squared loadings, while preserving the orthogonality of the loading matrix.
  2. The promax rotation, a method for oblique rotation, which builds upon the varimax rotation, but ultimately allows factors to become correlated.

This package includes a stand-alone Python module with a FactorAnalyzer() class. The class includes an analyze() method that allows users to perform factor analysis using either minres or MLE, with optional rotations on the factor loading matrices. The package also offers a stand-alone Rotator() class to perform common rotations on an unrotated loading matrix.


In [1]: import pandas as pd

In [2]: from factor_analyzer import FactorAnalyzer

In [3]: df_features = pd.read_csv('test02.csv')

In [4]: fa = FactorAnalyzer()

In [5]: fa.analyze(df_features, 3, rotation=None)

In [6]: fa.loadings
           Factor1   Factor2   Factor3
sex      -0.129912 -0.163982  0.738235
zygosity  0.038996 -0.046584  0.011503
moed      0.348741 -0.614523 -0.072557
faed      0.453180 -0.719267 -0.075465
faminc    0.366888 -0.443773 -0.017371
english   0.741414  0.150082  0.299775
math      0.741675  0.161230 -0.207445
socsci    0.829102  0.205194  0.049308
natsci    0.760418  0.237687 -0.120686
vocab     0.815334  0.124947  0.176397

In [7]: fa.get_uniqueness()
sex         0.411242
zygosity    0.996177
moed        0.495476
faed        0.271588
faminc      0.668157
english     0.337916
math        0.380890
socsci      0.268054
natsci      0.350704
vocab       0.288503

In [8]: fa.get_factor_variance()
                 Factor1   Factor2   Factor3
SS Loadings     3.510189  1.283710  0.737395
Proportion Var  0.351019  0.128371  0.073739
Cumulative Var  0.351019  0.479390  0.553129


  • Python 3.4 or higher
  • numpy
  • pandas
  • scipy


Contributions to FactorAnalyzer are very welcome. Please file an issue on GitHub, or contact if you would like to contribute.


You can install this package via pip with:

$ pip install factor_analyzer

Alternatively, you can install via conda with:

$ conda install -c desilinguist factor_analyzer


GNU General Public License (>= 2)

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