Orthogonal Rotation

A factor analysis technique transforming a solution into a more interpretable structure while constraining the resulting factors to remain uncorrelated.

Source: Kaiser 1958

Orthogonal rotation reworks a factor solution to make it easier to interpret while keeping the factors uncorrelated with one another. This constraint means each factor is treated as an independent dimension, which yields a clean, simple structure and coefficients that can be read straightforwardly. It suits situations where the underlying constructs are genuinely thought to be distinct, and its common form, varimax, sharpens each factor by pushing loadings toward high or low values. Keeping the factors independent is its defining constraint. Kline (2015) describes this technique.

Source: Kline 2015

Orthogonal rotation is used when the factors can reasonably be treated as uncorrelated, or when independent factors are wanted for simplicity of interpretation or for subsequent use, such as creating uncorrelated scores. So orthogonal rotation is used where independence of the factors is assumed or desired, giving a simple, easily interpreted structure with uncorrelated factors, which is convenient, though it may be less realistic than oblique rotation when the underlying constructs are actually correlated, so the choice depends on whether the factors are plausibly independent or the simplicity of uncorrelated factors is preferred despite possible correlation.

Source: Kaiser 1958

Orthogonal rotation constrains the rotated factors to remain uncorrelated, while oblique rotation allows them to correlate. Orthogonal rotation gives simpler, independent factors suited to constructs treated as unrelated, whereas oblique rotation suits correlated constructs and provides factor correlations. So the two differ in whether correlations among factors are permitted, with orthogonal rotation being simpler but assuming independence and oblique rotation more flexible and realistic for related constructs, and the choice depends on whether the underlying factors are expected to be correlated, with orthogonal rotation appropriate when independence is reasonable and oblique when the factors are related.

Source: Kaiser 1958

The advantages of orthogonal rotation include producing a simple, easily interpreted structure with uncorrelated factors, so each factor's contribution is distinct; yielding factor scores that are independent, which can be convenient for subsequent analyses; and being straightforward to apply and understand. So orthogonal rotation is advantageous for its simplicity and the independence of its factors, which makes interpretation and later use clean, particularly when the factors can reasonably be considered unrelated, though this same constraint is a limitation when the underlying constructs are actually correlated, in which case oblique rotation gives a more faithful representation despite its greater complexity.

Source: Kaiser 1958

The varimax method is a widely used orthogonal rotation that seeks a simple structure by maximising the variance of the squared loadings within each factor, which tends to make each variable load strongly on one factor and weakly on the others while keeping the factors uncorrelated. So the varimax method is a specific orthogonal rotation aimed at producing clear, interpretable factors with high and low loadings sharply separated, which is why it is a common default when orthogonal rotation is chosen, delivering a simple structure of independent factors, though, being orthogonal, it assumes the factors are uncorrelated, which may not suit all data.

Source: Kaiser 1958