EducationalTestingService/factor_analyzer

FactorAnalyzer

This is a Python module to perform exploratory and factor analysis (EFA), with several optional rotations. It also includes a class to perform confirmatory factor analysis (CFA), with certain pre-defined constraints. In exploratory factor analysis, factor extraction can be performed using a variety of estimation techniques. The factor_analyzer package allows users to perform EFA using either (1) a minimum residual (MINRES) solution, (2) a maximum likelihood (ML) solution, or (3) a principal factor solution. However, CFA can only be performed using an ML solution.

Both the EFA and CFA classes within this package are fully compatible with scikit-learn. Portions of this code are ported from the excellent R library psych, and the sem package provided inspiration for the CFA class.

Please see the official documentation for additional details.

Description

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.

Confirmatory factor analysis (CFA), a closely associated technique, is used to test an a priori hypothesis about latent relationships among sets of observed variables. In CFA, the researcher specifies the expected pattern of factor loadings (and possibly other constraints), and fits a model according to this specification.

Typically, a number of factors (K) in an EFA or CFA model 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 MINRES or ML.

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 the case of EFA, factor loading matrices are usually 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 factor_analyzer module with a stand-alone FactorAnalyzer class. The class includes fit() and transform() methods that enable users to perform factor analysis and score new data using the fitted factor model. Users can also perform optional rotations on a factor loading matrix using the Rotator class.

The following rotation options are available in both FactorAnalyzer and Rotator:

1. varimax (orthogonal rotation)
2. promax (oblique rotation)
3. oblimin (oblique rotation)
4. oblimax (orthogonal rotation)
5. quartimin (oblique rotation)
6. quartimax (orthogonal rotation)
7. equamax (orthogonal rotation)
8. geomin_obl (oblique rotation)
9. geomin_ort (orthogonal rotation)

In addition, the package includes a confirmatory_factor_analyzer module with a stand-alone ConfirmatoryFactorAnalyzer class. The class includes fit() and transform() that enable users to perform confirmatory factor analysis and score new data using the fitted model. Performing CFA requires users to specify in advance a model specification with the expected factor loading relationships. This can be done using the ModelSpecificationParser class.

Note that the ConfirmatoryFactorAnalyzer class is very experimental at this point, so use it with caution, especially if your data are highly non-normal.

Examples

Exploratory factor analysis example.

In [1]: import pandas as pd
   ...: from factor_analyzer import FactorAnalyzer

In [2]: df_features = pd.read_csv('tests/data/test02.csv')

In [3]: fa = FactorAnalyzer(rotation=None)

In [4]: fa.fit(df_features)
Out[4]:
FactorAnalyzer(bounds=(0.005, 1), impute='median', is_corr_matrix=False,
               method='minres', n_factors=3, rotation=None, rotation_kwargs={},
               use_smc=True)

In [5]: fa.loadings_
Out[5]:
array([[-0.12991218,  0.16398151,  0.73823491],
       [ 0.03899558,  0.04658425,  0.01150343],
       [ 0.34874135,  0.61452341, -0.07255666],
       [ 0.45318006,  0.7192668 , -0.0754647 ],
       [ 0.36688794,  0.44377343, -0.01737066],
       [ 0.74141382, -0.15008235,  0.29977513],
       [ 0.741675  , -0.16123009, -0.20744497],
       [ 0.82910167, -0.20519428,  0.04930817],
       [ 0.76041819, -0.23768727, -0.12068582],
       [ 0.81533404, -0.12494695,  0.17639684]])

In [6]: fa.get_communalities()
Out[6]:
array([0.5887579 , 0.00382308, 0.50452402, 0.72841182, 0.33184336,
       0.66208429, 0.61911037, 0.73194557, 0.64929612, 0.71149718])

Confirmatory factor analysis example.

In [1]: import pandas as pd

In [2]: from factor_analyzer import (ConfirmatoryFactorAnalyzer,
   ...:                              ModelSpecificationParser)

In [3]: df_features = pd.read_csv('tests/data/test11.csv')

In [4]: model_dict = {"F1": ["V1", "V2", "V3", "V4"],
   ...:               "F2": ["V5", "V6", "V7", "V8"]}
In [5]: model_spec = ModelSpecificationParser.parse_model_specification_from_dict(df_features,
   ...:                                                                           model_dict)

In [6]: cfa = ConfirmatoryFactorAnalyzer(model_spec, disp=False)

In [7]: cfa.fit(df_features.values)

In [8]: cfa.loadings_
Out[8]:
array([[0.99131285, 0.        ],
       [0.46074919, 0.        ],
       [0.3502267 , 0.        ],
       [0.58331488, 0.        ],
       [0.        , 0.98621042],
       [0.        , 0.73389239],
       [0.        , 0.37602988],
       [0.        , 0.50049507]])

In [9]: cfa.factor_varcovs_
Out[9]:
array([[1.        , 0.17385704],
       [0.17385704, 1.        ]])

In [10]: cfa.transform(df_features.values)
Out[10]:
array([[-0.46852166, -1.08708035],
       [ 2.59025301,  1.20227783],
       [-0.47215977,  2.65697245],
       ...,
       [-1.5930886 , -0.91804114],
       [ 0.19430887,  0.88174818],
       [-0.27863554, -0.7695101 ]])

Requirements

• Python 3.8 or higher
• numpy
• pandas
• scipy
• scikit-learn
• pre-commit

Contributing

Contributions to factor_analyzer are very welcome. Please file an issue in the repository if you would like to contribute.

Installation

You can install this package via pip with:

$ pip install factor_analyzer

Alternatively, you can install via conda with:

$ conda install -c ets factor_analyzer

License

GNU General Public License (>= 2)