Varimax rotation is an important second step in Factor Analysis and Principal Component Analysis. The initial factor analysis step has an infinite number of initial, or provisional, factors. Factor rotation, including Varimax rotation, transforms the initial factors into new ones that are easier to interpret.

## Factor Rotations

Factor rotations make the expression of a particular subspace simpler. Subspaces are smaller vector spaces within a R^{n} vector space. The orthogonal basis is rotated to align with the coordinate system, which is left unchanged.

Rotations can be orthogonal, like Varimax rotation, or oblique. With oblique factor rotations, the new factors are correlated; With orthogonal rotation, the factors are *not *correlated. Of the two types, orthogonal rotations have the “…greatest scientific utility, consistency, and meaning” (Gannon Cook, 2010). Varimax, along with quartimax, are two of the most common types of orthogonal rotations (Merenda, 1997).

## Varimax Rotation

Varimax rotation (also called Kaiser-Varimax rotation) maximizes the sum of the variance of the squared loadings, where ‘loadings’ means correlations between variables and factors. This usually results in high factor loadings for a smaller number of variables and low factor loadings for the rest. Remaining components all have eigenvalues of more than one (Stevens, 1996). In simple terms, the result is a small number of important variables are highlighted, which makes it easier to interpret your results.

## References

Gannon-Cook, R. (2010). What Motivates Faculty to Teach in Distance Education?: A Case Study and Meta-Literature Review. University Press of America.

Manly, B. (2004). Multivariate Statistical Methods: A Primer, Third Edition. CRC Press.

Merenda, Peter F. (1997). “A Guide to the Proper Use of Factor Analysis in the Conduct and Reporting of Research: Pitfalls to Avoid,” Measurement and Evaluation in Counseling and Development 30, 156-164

Stephens, D. (1996). . Hearing rehabilitation in a psychosocial framework. . Scandinavian Audiology , 25((Supplement 43)): 57

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