Data scientists typically use principal components analysis (PCA) as a data reduction tool. PCA and a related method, factor analysis (FA), can do much more than this, however.

Either method can also help us understand how the variables in our data interrelate. Rotation of components and factors is especially helpful in this regard.

Unfortunately, many data scientists never use rotation and many marketing researchers habitually use varimax orthogonal rotation.

Here are some other rotation methods, many with oblique variations which allow the components/factors to be correlated:

- GEOMIN
- QUARTIMIN
- QUARTIMAX
- EQUAMAX
- PARSIMAX
- PROMAX
- OBLIMIN
- OBLIMAX
- PROCRUSTEAN
- BI-FACTOR
- BENTLER
- CRAWFORD-FERGUSON

The eigenvalue >= 1 guideline for selecting the number of components or factors is not always best, either.

There are also numerous factor extraction methods that are seldom used even when they would be more appropriate.

Moreover, we are not bound to assume our data are continuous, and I often use variations of factor analysis designed for ordinal or nominal data.

There is also no need to assume one factor solution fits all - factor mixture modeling has rescued me on more than one occasion.

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