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An oblique rotation should not change how much of each item the factor model explains.
get_communalities()ignores factor correlations, so it can report impossible negative uniquenesses.Example
On the bundled 2,571-row questionnaire, a 3-factor promax model reports communality 1.103082 for one item (uniqueness −0.103082). Using the model’s structure matrix gives 0.590760 (uniqueness 0.409240). The maximum item error is 0.512322.
Fix
For oblique rotations, compute
row_sum(pattern * structure); retain squared loadings for orthogonal rotations. The regression checks that promax preserves the unrotated model-implied communalities.The full 102-test suite passes. Corrected values match the repository’s R
psychfixture within 2.2e-6.Evidence and exact commands: https://cheerfulduck.com/research/audits/factor-analyzer-oblique-communalities
Limits
This changes communalities, uniquenesses, and reduced-matrix eigenvalues, not fitted loadings or scores. No changed published conclusion was identified. No exact prior report was found after bounded issue/PR searches.