Summary: Factor Rotations in Factor Analyses.
The University of Texas at Dallas
The different methods of factor analysis first extract a set a factors from a
data set. These factors are almost always orthogonal and are ordered according
to the proportion of the variance of the original data that these factors explain.
In general, only a (small) subset of factors is kept for further consideration and
the remaining factors are considered as either irrelevant or nonexistent (i.e.,
they are assumed to reflect measurement error or noise).
In order to make the interpretation of the factors that are considered rel-
evant, the first selection step is generally followed by a rotation of the factors
that were retained. Two main types of rotation are used: orthogonal when the
new axes are also orthogonal to each other, and oblique when the new axes are
not required to be orthogonal to each other. Because the rotations are always
performed in a subspace (the so-called factor space), the new axes will always
explain less variance than the original factors (which are computed to be opti-
mal), but obviously the part of variance explained by the total subspace after
rotation is the same as it was before rotation (only the partition of the variance
has changed). Because the rotated axes are not defined according to a statistical