I am setting up a factor analysis with the Factor procedure, under Analyze->Data Reduction->Factor, and click on the Rotation button to choose a factor rotation method. If I click on Promax under Method, then the Kappa box becomes enabled. The pop-up Help box for Kappa says "Kappa is a parameter which controls the calculation of the promax rotation. The default value is 4. This value is appropriate for most analysis." Please provide a fuller description of how this Kappa parameter affects the promax rotation and how I would choose a value for Kappa.
Resolving The Problem
The basic approach of Promax is to start with an orthogonal rotation of the factor or component matrix, and raise the loadings to some power to produce an ideal or hypothesized factor matrix. Signs of loadings are restored and the unrotated factor matrix is then rotated to the best least squares fit to this ideal factor matrix. Kappa is the power to which the loadings are raised. When the loadings are raised to a Kth power, they are all reduced but the impact is more dramatic on the smaller loadings, bringing you closer to simple structure (each variable having a substantial loading on few factors, often ideally one factor). The factors also become correlated. Higher values of Kappa lead to higher correlations among factors and simpler structure of the loadings. The optimum Kappa is that value which gives the simplest structure with the lowest correlations among factors. The default value of 4 was recommended by its developers Hendrickson and White (1964) as generally providing a good solution. For SPSS Factor, Kappa must be a real value that is greater than or equal to 1.0.
Gorsuch, R. L. (1983). Factor Analysis (2nd Ed.). Hillsdale NJ: Erlbaum. (Chapter 9).
Hendrickson, A.E., & White, P.O. (1964). Promax: A quick method for rotation to oblique simple structure. British Journal of Statistical Psychology, 17(1), 65-70.
Also, see the Factor algorithms, available via Help>Algorithms>FACTOR Algorithms, for the implementation of promax rotation, including the Kappa parameter, in IBM SPSS Statistics.
16 April 2020