Troubleshooting
Problem
I am setting up a factor analysis with the SPSS Factor procedure, under Analyze>Data Reduction>Factor, and click on the Rotation button to choose a factor rotation method. If I click on 'Direct Oblimin' under Method, then the Delta box becomes enabled. The pop-up Help box for Delta says "When delta = 0 (the default), solutions are most oblique. As delta becomes more negative, the factors become less oblique. To override the default delta of 0, enter a number less than or equal to 0.8." Please provide a fuller description of how this Delta parameter affects the direct oblimin rotation and how I would choose a value for delta. If factors become less oblique as delta becomes more negative, and if solutions are 'most oblique' when delta = 0, what is the effect of a delta between 0 and 0.8? What is the basis for the upper limit of 0.8?
Resolving The Problem
The foundation paper for the direct oblimin rotation method is Jennrich and Sampson (1966). A detailed discussion is also available in Harman (1976) and some discussion is provided in Tabachnick & Fidell (2001). Also, see the Factor Rotations section in the FACTOR algorithms (Help>Algorithms>FACTOR Algorithms) for the implementation of direct oblimin rotation, including the delta parameter, in SPSS.
Harman (1976, p. 321) displays the formula for the criteria that is being minimized in the direct oblimin method, F(P). He notes that it is possible for this minimum to reach negative infinity if positive values of delta are used and cites a communication from Jennrich that F(P)approaches negative infinity if, and only if, delta is greater than .8. Thus, the upper bound for delta in SPSS Factor is .8. Harman suggests for practical purposes that 0 or negative delta values should be chosen. Within this suggested range of delta, the factors are most oblique when delta = 0. Using delta values between 0 and .8 will result in factors that are even more oblique, but the result may be factors that are so highly correlated (positively or negatively) as to be indistinguishable. Large negative values of delta will lead to factors which are nearly orthogonal. Of course, the correlations among the factors is limited by the data, as well as the choice of delta. There does not seem to be a single value of delta which provides the best solution for all data sets. See Harman's discussion of his experimentation with delta for several well-known data sets.
Harman, H. H. (1976). Modern Factor Analysis (3rd Ed.). Chicago : University of Chicago Press. (pp. 320-327).
Jennrich, R.I. & Sampson, P.F. (1966). Rotation for simple loadings. Psychometrika, 31, 313-323.
Tabachnick, B.G., & Fidell, L.S. (2001). Using Multivariate Statistics (4th Ed.). Boston: Allyn & Bacon. (p. 616).
Related Information
Historical Number
33361
Was this topic helpful?
Document Information
Modified date:
16 April 2020
UID
swg21475052