reliabiliPy

Summary

• Simple implementation in Python of the [reliability](https://en.wikipedia.org/wiki/Reliability_(statistics) measures for surveys: Omega Total, Omega Hierarchical and Omega Hierarchical Asymptotic and Omega Total, using Schmid-Leiman solution.
• Also Cronbach's Alpha Guttman’s lower bounds of reliability $\lamda_1$ and $\lamda_2$.
• Explanations and documentation available

See Documentation

Quick Start

If you have the correlations matrix of your dataset.

To install:

pip install reliabiliPy

To start using it:

import pandas as pd
import numpy as np
from reliabilipy import reliability_analysis

correlations_matrix = pd.DataFrame(np.matrix([[1., 0.483, 0.34, 0.18, 0.277, 0.257, -0.074, 0.212, 0.226],
                                              [0.483, 1., 0.624, 0.26, 0.433, 0.301, -0.028, 0.362, 0.236],
                                              [0.34, 0.624, 1., 0.24, 0.376, 0.244, 0.233, 0.577, 0.352],
                                              [0.18, 0.26, 0.24, 1., 0.534, 0.654, 0.165, 0.411, 0.306],
                                              [0.277, 0.433, 0.376, 0.534, 1., 0.609, 0.041, 0.3, 0.239],
                                              [0.257, 0.301, 0.244, 0.654, 0.609, 1., 0.133, 0.399, 0.32],
                                              [-0.074, -0.028, 0.233, 0.165, 0.041, 0.133, 1., 0.346, 0.206],
                                              [0.212, 0.362, 0.577, 0.411, 0.3, 0.399, 0.346, 1., 0.457],
                                              [0.226, 0.236, 0.352, 0.306, 0.239, 0.32, 0.206, 0.457, 1.]]))
reliability_report = reliability_analysis(correlations_matrix=correlations_matrix)
reliability_report.fit()
print('here omega Hierarchical: ', reliability_report.omega_hierarchical)
print('here Omega Hierarchical infinite or asymptotic: ', reliability_report.omega_hierarchical_asymptotic)
print('here Omega Total', reliability_report.omega_total)
print('here Alpha Cronbach total', reliability_report.alpha_cronbach)
print(reliability_report.lambda1)
print(reliability_report.lambda2)
print(reliability_report.report_eigenvalues)
print(reliability_report.report_loadings)

If you want to use the whole dataset you could do it to, adding the inputations method you prefer:

import pandas as pd
import numpy as np
from reliabilipy import reliability_analysis
raw_dataset = pd.DataFrame([{'C1': 2.0, 'C2': 3.0, 'C3': 3.0, 'C4': 4.0, 'C5': 4.0},\
        {'C1': 5.0, 'C2': 4.0, 'C3': 4.0, 'C4': 3.0, 'C5': 4.0},\
        {'C1': 4.0, 'C2': 5.0, 'C3': 4.0, 'C4': 2.0, 'C5': 5.0},\
        {'C1': 4.0, 'C2': 4.0, 'C3': 3.0, 'C4': 5.0, 'C5': 5.0},\
        {'C1': 4.0, 'C2': 4.0, 'C3': 5.0, 'C4': 3.0, 'C5': 2.0},\
        {'C1': 4.0, 'C2': np.nan, 'C3': 3.0, 'C4': 5.0, 'C5': 5.0},\
        {'C1': np.nan, 'C2': 4.0, 'C3': 5.0, 'C4': 3.0, 'C5': 2.0}])
ra = reliability_analysis(raw_dataset=raw_dataset,
                              is_corr_matrix=False,
                              impute='median')
ra.fit()
print('here omega Hierarchical: ', ra.omega_hierarchical)
print('here Omega Hierarchical infinite or asymptotic: ', ra.omega_hierarchical_asymptotic)
print('here Omega Total', ra.omega_total)
print('here Alpha Cronbach total', ra.alpha_cronbach)

Context

It is common to try check the reliability, i.e.: the consistency of a measure, particular in psychometrics and surveys analysis.

R has packages for this kind of analysis available, such us psychby Revelle (2017). python goes behind on this. The closes are factor-analyser and Pingouin. As I write this there is a gap in the market since none of the above libraries currently implement any omega related reliability measure. Although Pingouin implements Cronbach's alpha

Aim

1. To bring functions to python for psychometrics and survey analysis, as there is a gap. Mostly from the package in R psych.
2. To make the ideas and math behind those clear and transparent with examples, and documentation.
3. To allow people to collaborate and ask questions about.

References

• Flora, David B. "Your coefficient alpha is probably wrong, but which coefficient omega is right? A tutorial on using R to obtain better reliability estimates." Advances in Methods and Practices in Psychological Science 3.4 (2020): 484-501. https://journals.sagepub.com/doi/pdf/10.1177/2515245920951747
• Revelle, Willian. Manuscrip. 2021. An introduction to psychometric theory with applications in R. https://personality-project.org/r/book/Chapter7.pdf
• Revelle, William R. "psych: Procedures for personality and psychological research." (2017).
  • Omega Implementation in R. https://github.com/cran/psych/blob/master/R/omega.R
  • Schmid-Leiman in R. https://github.com/cran/psych/blob/master/R/schmid.R
• Starkweather, Jon (2013). Hierarchical Factor Analysis. https://it.unt.edu/sites/default/files/hierfa_l_jds_apr2013.pdf
• Vallat, R. (2018). Pingouin: statistics in Python. Journal of Open Source Software, 3(31), 1026, https://doi.org/10.21105/joss.01026
• Wolff, Hans-Georg, and Katja Preising. "Exploring item and higher order factor structure with the Schmid-Leiman solution: Syntax codes for SPSS and SAS." Behavior Research Methods 37.1 (2005): 48-58.

Acknowledgement

• Factor Analyzer. Python library. This library is based heavily on this one. https://github.com/EducationalTestingService/factor_analyzer

Cite this package as

• Rafael Valero Fernández. (2022). reliabiliPy: measures of survey domain reliability in Python with explanations and examples. Cronbach´s Alpha and Omegas. (v0.0.0). Zenodo. https://doi.org/10.5281/zenodo.5830894

or

@software{rafael_valero_fernandez_2022_5830894,
  author       = {Rafael Valero Fernández},
  title        = {{reliabiliPy: measures of survey domain reliability 
                   in Python with explanations and examples.
                   Cronbach´s Alpha and Omegas.}},
  month        = jan,
  year         = 2022,
  publisher    = {Zenodo},
  version      = {v0.0.0},
  doi          = {10.5281/zenodo.5830894},
  url          = {https://doi.org/10.5281/zenodo.5830894}
}

Happy to modify the above as petition and contributions.