Factor Analysis as a Classification Method - Oblique Factors

Some authors (e.g., Cattell & Khanna; Harman, 1976; Jennrich & Sampson, 1966; Clarkson & Jennrich, 1988) have discussed in some detail the concept of oblique (non-orthogonal) factors, in order to achieve more interpretable simple structure.

Specifically, computational strategies have been developed to rotate factors so as to best represent "clusters" of variables without the constraint of orthogonality of factors. However, the oblique factors produced by such rotations are often not easily interpreted.

Considering the Factor Analysis Example 1, suppose we would have included in the satisfaction questionnaire four items that measured other, "miscellaneous" types of satisfaction. Let's assume that people's responses to those items were affected about equally by their satisfaction at home (Factor 1) and at work (Factor 2). An oblique rotation will likely produce two correlated factors with less-than-obvious meaning, that is, with many cross-loadings.