oblimin

Oblimin is a rotation method used in exploratory factor analysis and principal component analysis to produce a simpler, more interpretable loading pattern while allowing the extracted factors to be correlated. It belongs to the family of oblique rotations, which contrast with orthogonal rotations by permitting factor correlations. The rotation is parametric, controlled by a gamma value that shapes the objective function used to rotate the loading matrix. Different gamma settings yield different emphases on simple structure versus allowing cross-loadings, giving researchers a way to tailor the rotation to their data.

In practice, oblimin is implemented in many statistical software packages (for example, rotate="oblimin" in R’s psych package, as well as in SPSS, SAS, and Mplus). After rotation, results commonly include the pattern matrix (the regression loadings of variables on factors) and the structure matrix (the correlations between variables and latent factors), as well as a factor correlation matrix that shows how the rotated factors relate to one another.

Interpreting oblimin results requires attention to factor correlations and cross-loadings. Because the rotation is oblique, factors are not orthogonal, and loadings may appear on multiple factors. Researchers compare oblimin results with other rotations (such as promax or direct oblimin variants) to check robustness. When theoretical constructs are expected to be related, oblimin offers a flexible alternative to orthogonal rotations, whereas orthogonal rotations may be preferred if independent factors are assumed.