Unrotated results from a factor analysis—as presented in Chapter 3—are not easy to interpret. Factor loading plots can help, but they can still present a rather confusing picture, particularly if there are more than two factors! Rotation was developed not long after factor analysis to help researchers clarify and simplify the results of a factor analysis. Indeed, early methods were subjective and graphical in nature (Thurstone, 1938) because the calculations were labor intensive. Later scholars attempted to make rotation less subjective or exploratory (e.g., Horst, 1941), leading to initial algorithms such as quartimax (Carroll, 1953) and varimax (Kaiser, 1958). Although varimax was introduced early on, it is still one of the most widely used methods of rotation (perhaps because it is the default in much statistical software).[1]

Quite simply, we use the term “rotation” because, historically and conceptually, the axes are being rotated so that the clusters of items fall as close as possible to them.[2] As Thompson (2004) notes, the location of the axes is entirely arbitrary, and thus we can rotate the axes through space (like turning a dial) without fundamentally altering the nature of the results. However, we cannot move the location of any variable in the factor space.

Look at the left plot in Figure 4.1 Example of unrotated and rotated factor loading plot from engineering data, for example. If you imagine rotating the axes so that they intersect the centroid of each cluster of variables, you get the rotated factor pattern presented on the right, and you also get the essence of rotation. You might be wondering what that does for us in terms of clarifying the factor loadings. When we make that rotation, the factor pattern coefficients also have now changed, with some getting larger, and some getting smaller. As you can see in the rotated factor plot, the items now fall closely about each axis line. This has the effect of making the factor loading pattern much clearer, as one of the two pairs of coordinates for each item tends to be close to 0.00.