Factor Analysis as a Classification Method - Rotating the Factor Structure

We could plot the factor loadings shown above in a scatterplot. In that plot, each variable is represented as a point. In this plot we could rotate the axes in any direction without changing the relative locations of the points to each other; however, the actual coordinates of the points, that is, the factor loadings would of course change. In this example, if you produce the plot it will be evident that if we were to rotate the axes by about 45 degrees we might attain a clear pattern of loadings identifying the work satisfaction items and the home satisfaction items.

Rotational strategies. There are various rotational strategies that have been proposed. The goal of all of these strategies is to obtain a clear pattern of loadings, that is, factors that are somehow clearly marked by high loadings for some variables and low loadings for others. This general pattern is also sometimes referred to as simple structure (a more formalized definition can be found in most standard textbooks). Typical rotational strategies are varimax, quartimax, and equamax; these are described in greater detail in the context of the Rotation dialog.

We have described the idea of the varimax rotation before (see Extracting Principal Components), and it can be applied to this problem as well. As before, we want to find a rotation that maximizes the variance on the new axes; put another way, we want to obtain a pattern of loadings on each factor that is as diverse as possible, lending itself to easier interpretation. Below is the table of rotated factor loadings.

STATISTICA

FACTOR

ANALYSIS

Factor Loadings (Varimax normalized)

Extraction: Principal components

 

Variable

Factor 1

Factor 2

WORK_1

.862443

.051643

WORK_2

.890267

.110351

WORK_3

.886055

.152603

HOME_1

.062145

.845786

HOME_2

.107230

.902913

HOME_3

.140876

.869995

Expl.Var

2.356684

2.325629

Prp.Totl

.392781

.387605