Varimax and Oblique Factor Rotation

Factor analysis extracts a small number of latent factors that explain the correlations among many observed variables, but the initial loadings it spits out are arbitrary in a specific sense: you can rotate the factor axes by any angle and the model fits the data exactly as well as before, because only the subspace the factors span is pinned down by the data, not any particular orientation within it. Left unrotated, loadings are often messy — every variable loads moderately on every factor, telling you little about what each factor "means." Rotation methods search over these equally-valid orientations for the one that is easiest to read.

Varimax is the standard orthogonal rotation: it keeps the factors uncorrelated with each other while maximizing the variance of squared loadings within each factor, which pushes loadings toward either near-zero or near-one — each variable ends up clearly tied to one factor rather than smeared across several. Oblique rotations (like promax or direct oblimin) relax the uncorrelated-factors constraint, letting the factors themselves correlate, which usually gives an even cleaner "simple structure" when the underlying latent constructs are genuinely related — for instance, value and quality factors in an equity risk model plausibly overlap rather than being orthogonal by assumption.

If ten valuation and profitability ratios load messily across two unrotated factors, a varimax rotation will typically leave one factor loading almost entirely on the valuation ratios and the other almost entirely on the profitability ratios, with near-zero cross-loadings — the same fit, a far more interpretable factor.