Overview
EFA explores a common-factor representation when the latent structure is not fixed in advance. It is not principal component analysis.
Theoretical foundation
The common-factor model represents the observed covariance matrix as common-factor covariance plus unique variance. KMO compares squared correlations with squared partial correlations; Bartlett’s test evaluates departure from an identity correlation matrix. Parallel analysis compares observed eigenvalues with random-data eigenvalues.
Key equations
\Sigma=\Lambda\Phi\Lambda^\top+\PsiAlgorithm and computation
Survlytics uses complete numeric cases, Pearson correlations, statsmodels Factor extraction with squared multiple-correlation initial communalities, optional orthogonal varimax rotation, and seeded normal-data parallel analysis. KMO and Bartlett statistics are computed directly. Requested factors must be fewer than indicators; uniquenesses are checked for Heywood or inadmissible values.
Required data
At least three varying numeric indicators and at least max(30, five times the indicator count) complete observations.
Assumptions
A common-factor explanation must be substantively plausible. Maximum-likelihood extraction has stronger distributional assumptions. Orthogonal varimax assumes uncorrelated rotated factors.
Available settings
Principal-axis or maximum-likelihood extraction as supported by statsmodels; factor count; none or varimax rotation; parallel-analysis samples and random seed.
Worked example
Synthetic indicators are screened with KMO and Bartlett evidence, then a two-factor solution is compared with the 95th percentile parallel-analysis eigenvalues. Interpretation considers wording and cross-loadings.
Limitations and non-claims
Ordinal indicators still use Pearson correlations; polychoric EFA and oblique rotation are not implemented. Parallel analysis uses normally generated random matrices.
Validation notes
Factorability, extraction safeguards and seeded parallel analysis are unit-tested. No claim of equivalence to every EFA package or rotation convention is made.
How Surv.lytics computes Exploratory factor analysis
{'rotation': 'varimax'}References and verification status
Horn, J. L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrika, 30(2), 179–185. https://doi.org/10.1007/bf02289447
VerifiedOpen DOIKaiser, H. F. (1974). An index of factorial simplicity. Psychometrika, 39(1), 31–36. https://doi.org/10.1007/bf02291575
Unverified draftOpen DOI
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